“Break glass in case of emergency”.

It will say how many days you must wait until you legally use a locksmith to enter in your units under emergency.

I was looking at putting 20% down on a 2-4 unit building in a smaller emerging market where i can afford to put that much down.

These were not emergency instances, and there was no maintenance being done when he came inside- it appears he's simply "curious".  

It's annoying when they're making easily avoidable mistakes or make mistakes on things they really should be much more careful about, though.I try to minimize "emergencies" in house by keeping track of milestones so that we have more time to address the emergencies caused by our vendors, haha!

Sometimes , as in exhibit 2 you attached, the Contractor has to make a judgement call and go ahead because of emergencies or weather, but this should be rare.

Preferably 30 minutes away from Arlington Heights where I work (I work in a hospital that requires I live close enough so that if I need to come in during an emergency, I can arrive in less than 37 minutes).

My husband feels we shouldn’t risk using the money in case of emergency.

That may get them to respond, if not, follow through and enter and if need be have the city or non emergency services enter to do a health and safety check. 

(could have an emergency lockbox with physical key accessible)For long term renters, give them a  physical key.