Smart thieves would take the whole wallet, not remove money and leave fingerprints.

This is identical to a HELOC.

Offer that amount and don't go a penny more.Listing agents will lie, cheat, and thieve as much as they can.

Also, the UK is very much an exception to the rule as identity is checked in most European countries with national identity cards.

FIRST establish your investor identity; what type of deals do you want to get involved in (flips, wholesales, buy & hold, rent to own, etc), what type of property do you want to invest in (single family homes, multi family, commercial, etc), what's your risk tolerance, what sort of returns do you expect to get, do you want to be hands on or make it as passive as possible, etc.SECOND pick a strong market based on it's ability to meet your investor identity and based on strong fundamentals like I mentioned above.THIRD put together your team in that market.

I can't afford (literally) to have thieves or druggies around any more. 

If they give you a phone number for their work or supervisor, google the business and ask for the HR dept, instead of using the name and number they gave you.Any lies or discrepancies they give you are valid reasons to deny them.Pay for every single type of check you can do on them, credit/background/criminal/eviction/identity, etc. 

I want this second line to be effectively identical to a second cell phone.  

But, you can require proof of their identity and financial status, etc.

I sold a place in 2008 for $80,000, recently sold the identical property next door for $32,000, which is a 60% drop in value in 6 years!