I don’t understand. on the one hand, you were cutting, but on the other, your diet was bad? AND you weren’t going to the gym?
Dude. That means you weren’t cutting.
Of course you can gain your strength back. Have you tried things like working out and eating right? I bet that would go a long way.
Honestly, instead of approaching it as being ‘on a cut’ or ‘on a bulk’, just adopt healthy eating habits. Make these long term habits. And lift consistently. Everything falls into place much more easily when you don things this way. I’m never cutting, and I’m never bulking, I’m just always getting better.