If someone owns a house that is not paid off (still mortgaged), can someone buy it by taking another mortgage? What kind of offer would be most sensible? I assume that in this case the current owner of the house would want to make a profit.
Just as a renter doesn't care what the landlord's mortgage is, the buyer of a house shouldn't care what the seller paid, what the current mortgage is, or any other details of the seller's finances.
Two identical houses may be worth $400K. One still has a $450K loan, the other is mortgage free. You would qualify for the same value mortgage on both houses. All you and your bank should care about is that the present mortgage is paid or forgiven by the current mortgage holder so your bank can have first lien, and you get a clean title.
To answer the question clearly, yes, it's common for a house with a mortgage to be sold, mortgage paid off, and new mortgage put in place. The profit or loss of the homeowner is not your concern.
If someone owns a house that is not paid off...can someone buy it by taking another mortgage?
Yes, but I'm not sure why you think the buyer would need to take another mortgage to buy it. If someone sells their home for X dollars, then the buyer needs X dollars to buy the house. How they get that money (use cash, take out a mortgage) is up to them.
During the closing process, a portion of the funds generated from the sale are diverted to pay off the seller's loan and any leftover funds after closing are pocketed by the seller.
What kind of offer would be most sensible? I assume that in this case the current owner of the house would want to make a profit.
The amount that the house is sold for is determined by the market value of their home, not by the size of the mortgage they have left to pay off. You make the same offer whether they own their home or have a mortgage.
Pricing a house
Go on a website that has real estate listings. Find similar homes in the same neighborhood and list out the prices. Once you have prices, pick out two with different prices and call the realtor of the more expensive listing. Tell that realtor about the other listing and ask why their listing is more expensive. Compare their answer to the home that you are considering buying.
For example, they may say that their house has a newly remodeled kitchen. Does the house you are considering have a newly remodeled kitchen? If so, then use the higher priced listing and throw out the cheaper one. If not, use the cheap listing and throw out the expensive one.
Or they might say that the expensive house is in a better location than the cheaper house. Further away from traffic. Easier to get to the highway or public transportation. If so, ask how the location compares to the house you are actually considering. The realtor will tell you if the listings are comparable.
When I talk about "similar homes," I mean homes that are similar in square footage, number of bedrooms, and number of bathrooms. Generally real estate sites will allow you to search by all of these as well as location.
After all this, the potential seller may still turn you down. If he really wanted to sell, he'd have suggested a price. He may just be seeing if you're willing to overpay. If so, he could turn down an otherwise reasonable offer. How much he is willing to take is up to him.
Note that this would all be easier if you just bought a house the normal way. Then the realtors would do the comparables portion of the work. You might be able to find a realtor or appraiser who would do the work for a set fee. Perhaps your bank would help you with that, as they have to appraise the property to offer a mortgage.
Buying a mortgaged house
You asked if you can buy out a mortgaged house with a mortgage. Yes, you can. That's a pretty normal occurrence. Normally the realtors would make all the necessary arrangements. I'm guessing that a title transfer company could handle that.
Based on what you asked and your various comments on other answers, this is the first time that you will be making an offer to buy a house, and it seems that the seller is not using a real-estate agent to sell the house, that is, it is what is called a FSBO (for sale by owner) property (and you can learn a lot of about the seller's perspective by visiting fsbo.com). On the other hand, you are a FTB (first-time buyer) and I strongly recommend that you find out about the purchase process by Googling for "first-time home buyer" and reading some of the articles there. But most important, I urge you
DO NOT make a written offer to purchase the property until you understand a lot more than you currently do, and a lot more than all the answers here are telling you about making an offer to buy this property. Even when you feel absolutely confident that you understand everything, hire a real-estate lawyer or a real-estate agent to write the actual offer itself (the agent might well use a standard purchase offer form that his company uses, or the State mandates, and just fill in the blanks). Yes, you will need to pay a fee to these people but it is very important for your own protection, and so don't just wing it when making an offer to purchase.
As to how much you should offer, it depends on how much you can afford to pay. I will ignore the possibility that you are rich enough that you can pay cash for the purchase and assume that you will, like most people, be needing to get a mortgage loan to buy the house. Most banks prefer not to lend more than 80% of the appraised value of the house, with the balance of the purchase price coming from your personal funds. They will in some cases, loan more than 80% but will usually charge higher interest rate on the loan, require you to pay mortgage insurance, etc. Now, the appraised value is not determined until the bank sends its own appraiser to look at the property, and this does not happen until your bid has been accepted by the seller. What if your bid (say $500K) is much larger than the appraised value $400K on which the bank is willing to lend you only $320K ? Well, you can still proceed with the deal if you have $180K available to make the pay the rest. Or, you can let the deal fall apart if you have made a properly written offer that contains the usual contingency clause that you will be applying for a mortgage of $400K at rate not to exceed x% and that if you can't get a mortgage commitment within y days, the deal is off. Absent such a clause, you will lose the earnest money that you put into escrow for failure to follow through with the contract to purchase for $500K. Making an offer in the same ballpark as the market value lessens the chances of having the deal fall through. Note also that even if the appraised value is $500K, the bank might refuse to lend you $400K if your loan application and credit report suggest that you will have difficulty making the payments on a $400K mortgage. It is a good idea to get a pre-approval from a lender saying that based on the financial information that you have provided, you will likely be approved for a mortgage of $Z (that is, the bank thinks that you can afford the payments on a mortgage of as much as $Z). That way, you have some feel for how much house you can afford, and that should affect what kinds of property you should be bidding on.