Belts and hoses rarely fail without warning. A drive belt may squeal on a cold morning weeks before it snaps, and a coolant hose may seep for a while before it splits. The hard part is not spotting the warning. The hard part is deciding who looks, how often they look, and who acts when something seems wrong.
Start with a short check you can do in a few minutes with the engine off and cool. Look at the drive belts for cracks, fraying, a shiny glazed surface, or a loose feel when you press on the longest run. Look at the hoses for bulges, soft spots, cracks, or wet residue near the clamps. Check the engine bay for any new drips on the ground under the car. Never open the coolant system while the engine is hot.
Ownership is where most people get stuck. Decide who does the check. If you do it, keep a simple log with the date, the odometer reading, what you saw, and what you did about it. If a shop checks the belts and hoses during a routine visit, ask that the inspection be written on the invoice, not just said out loud at the counter. A spoken reassurance is hard to prove later.
Many service contracts state that the owner must keep up routine maintenance, and some ask for proof that the work was done. Find that clause before you buy. Look for words such as maintenance, records, proof, and wear, and note whether the contract tells you what kind of record counts. If a failure is later traced to a part nobody inspected, you want to know ahead of time how the provider handles it.
Ask the provider to explain its maintenance requirement in writing. The answer should name the items, the records you must keep, and the consequences if you miss a requirement. The providers that post a sample contract on this site let you read this language before you commit, which is the easiest place to check it.