Cohabitation can be a factor in divorce in Illinois. Cohabitation agreements are not an option for unmarried couples in Illinois, and are not legally recognized unless one party is going through a divorce, in which case dire consequences can occur.
Texas does not have alimony, so cohabitation is irrelevant. Very occasionally, temporary spousal maintenance will be awarded, which is limited in time to allow the ex-spouse to gain education or experience necessary to make ends meet. Cohabitation would not affect spousal maintenance.