Texas law does make a spouse liable for the necessary expenses their spouse incurs. Thus, the inheritance, which is considered separate property, can be subject to a creditor's claim for nonpayment of neccessaries provided to the other spouse. However, if you are not married at the time of the expense is incurred, then there is no liability. Thus, you may want to consider getting a divorce prior to any further expenses being incurred (which would be an extreme choice but would allow you to maintain control of the funds) or having your inheritance placed into a trust that would limit a creditor's ability to reach it.
You should go see an estate planning/asset protection attorney to discuss these options and others to determine your best course of action.
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Your parents should consult a CT lawyer and ask him to draft them Wills that create a type of trust that would protect your inheritance from your and your husband's creditors. That is done all the time. It is a much better solution that getting a divorce.
DISCLAIMER: This is not specific legal advice and does not establish an attorney/client relationship.
Your problem is not difficult to solve if your parents are willing to revise their estate plan to create an irrevocable trust for your benefit, with a spendthrift provision and a carefully drafted distribition provision-- so that the Trustee in its sole absolute discretion may distribute such amounts of income oe principal as are in your best interests is a good starting point. The Trustee should be an Independent Trustee as described in Subchapter J of the Internal Revenue Code. An experienced CT Trust and Estate Attorney can tweak this general concept to comply with CT law.