Can Mortgages Be Assumed?

Well, it depends. First, let's define "assumption". Assumption means that you're selling your home and the buyer wants to take over your mortgage with all its terms and conditions. Same interest rate, term length and payment.
Government Loans which are FHA, VA, and USDA loans can be assumed. Any non-government loans so Conventional Loans or any Non-QM loans cannot be assumed.

VA Loans: We do not recommend VA sellers to assume their mortgage to a buyer. The VA seller will be responsible for the new buyer’s payment if they default, and their VA benefits are tied into that home. It will also hurt their buying power when they to purchase a new home.
FHA Loans: FHA loans can be a good candidate for assuming a mortgage, but their downside is that the mortgage insurance will last the life of the loan unlike conventional loans.

Pros
Lower Interest Rate
Cheaper Closing Costs
No Appraisal
Cons
Higher Down Payment
Credit and Income Requirements