"Sleep Well At Night" Emergency Savings

[L'aura Bradford]

Hi all, what's the term commonly used for that emergency fund one should keep to cover mortgages on rental properties if they're vacant?  Some of the folks I've talked to in my local area call it a "sleep well at night" (SWAN) fund.

And what are some rules you follow?  I haven't been diligent about it and we just picked up our second rental so I figured it's a good time to put more thought into it.