The refrigerator in one of my units quit working last Friday.

I keep 2 refrigerators to have as emergency replacements to hold them over till I buy a new one  or when I am having a party to hold more beer .

For instance, you mentioned a refrigerator going out.

Because this property sat vacant for a couple months, it was broken into and appliances were stolen (refrigerator and washer/dryer - all brand new).

If it is in the current year, I note the month, as "new refrigerator 5/2014".

Think wire hangers to fix the toilet flapper, grey tape on the refrigerator and washing machine seal. 

The portion of repairs that applies to increase in valuation is the relief or discount in taxes (ie: they won't give you all the taxes off only the part of cost to repair real estate - does not include refrigerator, washer, dryer, any personal property... but a roof, or plumbing or structure yes) It's a good and wonderful discount.

Not sure how big you mini frig is, but if it's really small, I'd put a bigger refrigerator in there, like a 4-8 cubic size.   

Refacing works if you intend to leave the kitchen, dishwasher, sink and refrigerator in their existing locations.

Is the refrigerator supposed to fit in that hole?