Hard to get anything like this there .My first impresion was that bad standing with one creditor influences the credit card issuer but looks to me that it can not be imposed retroactively.
I checked this special offer terms and nothing like this is specified in this special offer balance transfer.
There is default term
clause that rises this promotional offer interest rate but in case of default with this lender (late payment,dishonor check overlimit etc) not a different one.
By the same token ,forclosure on rental property should not affect any other (owner ocupied unless there is significant equity involved)