Much like any other idea that sprouts from my head this one will be pretty vague too. I like to put up the most important details and then go over it with you to complete the setting.
I was thinking of a modern setting where MC is a cop or fireman and YC works in a hospital or something along those lines. The reason for the apocolyps could be either a disease (think zombies or a lethal virus) or war.
They meet when MC drops off a suspect at the hospital for a checkup (maybe they're high on drugs or something) and they start talking and hit it off.
It might be that the hospital starts sounding the alarm and MC's dispatcher starts warning every cop on duty about bombs or attacks OR (and this could also very well happen a few days later) there are people brought in that show signs of an unknown disease.
Either way they end up teaming up together and try and make it out alive.
Hit me up if you're interested!