The TBO hours and the calendar hours are manufactures recommendations. Most NAAs require that these recommendations are followed when the aeroplane is used for anything other than private use. However, there is usually a 20% extension available whatever the use and this period is known as 'on condition'. This is overseen by a licenced engineer and requires, typically, an inspection every 50 hours. When the aeroplane is used for private use only there are no limits to the on condition period, including a 12 year limitation.
If by example you bought a C150: the TCM 0-200 engine has a TBO of 1800 hours + 20% extension so totaling 2160 hours for professional use. What is most important for your situation is that the aircraft has been well maintained and that all ADs have been fully complied with. A survey is most important to confirm that the condition of the engine and the aeroplane generally is unlikely to require expensive maintenance in the foreseeable future. It is wise as a buyer to value the aeroplane based on the manufacturers TBO recommendations. It will be rarely viable to do any major repairs to a time expired engine. The only reasonable option could be a total rebuild/overhaul or a replacement. The seller of course will see it differently and may wax lyrical over the known reliability of the engine and that it could go on forever.