This question provides a mess to sort through using a few legal answers to numerous weighty questions. The wife/lady friend will not be liable for your debts but you will. I cannot predict how immigration law will operate 5/10 years from now but judging by how it's going, you'll be barred from returning until all your debts are paid.
IRS cannot take your wife's income or assets for your debts unless she puts the funds/assets into a joint account with you in which case her assets are avaialble to pay your debts. Also filing tax returns on a married-joint basis is not advisable.
My answer is not intended to be giving legal advice and this topic can be a complex area where the advice of a licensed attorney in your State should be obtained. Please click "helpful" or "best answer" if my answer added any value or add a "comment" if you have more info for me to help you get a better answer.
The other attorneys are correct. If you do not resolve your past due debts, you will have a difficult time obtaining U.S. permanent residency status 5 or 10 years from now. Also, as my immigration law colleague aptly noted, the standards for being admitted to the U.S. are becoming increasingly stringent. I suggest that you get your financial house in order and settle up your past-due debts (especially your potential personal liability for your former U.S. company's unpaid taxes, see IRC Sec. 6672) before you seek permanent U.S. residency. Congratulations on your upcoming nuptials!
The answer to this question does not establish an attorney-client relationship. Moreover, this attorney is licensed to practiced law ONLY in the State of California. Answers to questions from users in other jurisdictions or states are meant to provide only general information. Users should contact a local attorney in their jurisdiction or state to address their specific tax issue.