These are typically one-offs and depository institutions are in the best position to offer them.

effectively, you'd either need to look for a lender that would let you use the other property as collateral (cross) so that you can avoid actually taking the cash-out (this is rare in terms of institutional DSCR lenders, but fairly common in the hard money or private money space)...

There is a lot of uncertainty in the market for institutional capital, which funds a lot of these types of loans. 

Your current Lease and payment terms are recognized until [DATE]; however, moving forward, please send all payments, maintenance requests, and correspondence to the address listed at the top of this letter.If you are currently using an automatic draft, cash deposit, or other form of payment to pay for your residency, please contact your financial institution immediately so as to avoid any late fees and/or eviction notices.I have included with this letter a Tenant Update Form for you to fill out.

Also, at what point do institutional buyers re-enter the market aggressively. 

(outside of going after your personal assets) Banks and financial institutions are too smart to be putting themselves in this type of scenario.  

I've worked in institutional single family acquisitions for a few years and have rarely had good experiences with turnkey investors.

Be aware of Massachusetts Laws.

I am not sure about Massachusetts. 

I'm based in Western Massachusetts (Berkshire County) area.