Assumption is attractive mainly when the existing rate is well below current rates, since the buyer effectively steps into that rate along with the remaining balance and term, rather than starting a new mortgage from scratch.
The lender will requalify the buyer on income, credit and the property itself, exactly as if it were a new application, and a real estate lawyer handles the paperwork that moves title through the Information Services Corporation system, typically for $800 to $1,500 in legal fees.
Not every mortgage allows assumption, and not every lender wants to keep an old rate on its books, so this needs to be confirmed with the seller's lender early rather than assumed to be available. Get your hand-reviewed valuation from Joel Dyck.