The pronoun "quien" is only really used following a preposition or a comma, so in the majority of cases you need to use "que". For example: Me encontré con el anciano de quien te hablé ayer. Or: Tu hermano, a quien yo aprecio mucho, vino a verme. But in the type of sentence you have written, where the secondary clause is not preceded by a preposition, you have to use "que".

Use "que" is more natural, "quien" is more formal

Según mi marido español,la manera correcta es: "Mario era un aciano que podía cuidar de si mismo."

Use "que" is more natural, "quien" is more formal