Am I allowed to take out a personal loan to fix up my mother's basement for me to live in? How do loans work in this situation? Any help would be appreciated. Thanks!
You can take out a personal loan for any reason - to burn the money for fun, if you like.
But be aware that you owe it back, not your mother, or anyone else. They will come to you for the repayments.
It sounds like you may need to look into the different types of personal loans that are available to you. Typically, they are in 2 categories: secured vs unsecured. A personal loan is usually of the unsecured variety, meaning that the bank is loaning you money with no collateral to use if you default. These loans will have much higher interest rates than a secured loan. A prime example of a secured loan would be a mortgage or an equity line of credit.
If you want an unsecured personal loan to use towards making those improvements, then whether or not you receive the loan will depend on your credit rating and income status. As Aganju stated, these loans don't really care what the money is used for.
Because it's not your property that you're fixing up, you won't be able to get a secured loan against that property. If your mother took out a loan against her home (like a second mortgage), she may be able to get a significantly lower interest rate than what you'll get with an unsecured loan. She could also look into a renovation/remodeling loan, which would require information regarding the work being done such as costs and how it will improve the value of the property. If she used an equity line of credit instead, then they don't typically care what the money will be used for as it's just a credit line against the equity she's already built into her mortgage payments over the years.