Using mortgage as a protection tool on your rental properties

I have several residential rental properties with no mortgages on them. In addition to putting each one in an LLC As a protection against lawsuits, could one of the benefits of pulling cash out of the properties to reinvest , be not having equity in a particular property for charge orders or a tenant trying to sue for the equity (control) in that particular property?

So another words , if an attorney that takes on a tenants lawsuit sees a particular property is not free and clear and in fact has a first lienholder a.k.a. the mortgage company/bank— Will that property be passed up by the attorney bringing the lawsuit or will the attorney just go for the low hanging fruit (the insurance liability on the property? ) Will the bank in effect Block the lawsuit because the lawyer cannot take money

from the bank