Would I have to worry about any tax liability? it would not be like he
is "giving me" the house as I would be assuming the mortgage.
He would be selling you the house.
Also wondering who the title of the house goes to when someone else
assumes a mortgage.
You would be the owner.
If I were to assume the mortgage from him how would that work?
If you were to do go down this path. You would negotiate a price for the sale. It could be anything you both agree to. It could be equal to the mortgage balance.
The lender would have to agree to this. Some don't want to deal with it and don't allow somebody else to assume the mortgage. If the original mortgage does allow this they will have to approve you for that mortgage. They would look at your credit history, income, and other debts.
They are part of the approval process because the ownership paperwork filed with the government includes their lien on the property.
Now the taxes. I am assuming the United States.
If the sale results in a profit they may owe taxes. You said they are 5 years into the mortgage, so if it was the principal residence for that time, then they can shield 250K if they are single, or 500K if they are married, from capital gains taxes. If they rented it out, or they owned multiple houses the tax situation is more complex.
Of course if they sell below the market rate, the IRS could consider the difference as a gift to you.
he's behind on the mortgage payments, and he wants to get rid of the
house, but doesn't have the time or energy to clean it out and sell
The question will be how much time does he have before the lender seizes the property, and sells it. When they do that the equity your brother has can be wiped out. The fact he is are behind might make the lender block any attempt for you to assume the mortgage. A straight up sale would allow them to exit the situation. Foreclosing and trying to sell the property might take some time.