If I have The Last of Us (or any digital download for a game) attached to my account and I give someone else access to this account, and they access it through their system as if it was their own account, would they have access to the downloadable games?

Lets say I'm selling my system and want to give away everything (including the PS+ and digital downloads), which are attached to my account, by giving the account details can the other person access these things as I was able to?

Your account can be linked to a finite number of consoles. So in the case of selling the system with the account, yeah no worries. Bit selling your account to multiple people will have issues.

ok thanks
someone contacted me already but said it wouldn't work cause he "tried it with his friend's" and that "something wasn't available" or whatever
not sure if it was the case that there were multiple people or if he was clueless or if he just wanted to make me think it didn't work

they should as long as they dont delete your account

Most likely trying to gameshare in which there are more steps involved in which is the primary user etc etc.