Married or not, he can file bankruptcy on his own. Assuming he wants to file his own individual bankruptcy prior to the marriage, the joint accounts are only part of the bankruptcy estate to the extent that the funds in the accounts are his; the usual presumption in this situation is that joint accounts are 50-50, but this can be overcome with an affidavit or other evidence.
Does it affect you if you get married? Well, if you apply for a loan together, like a mortgage, it does not mean you will not get it, but it is extremely likely that the interest rate will be higher.
Can they take your joint assets? You need to clearly delineate (a) what is yours and what is his and (b) whether everything that is his is covered by available exemptions. What is clearly yours and provable as such is not part of the bankruptcy estate. What is his and covered by exemptions will not be taken away.
Is it necessary to close and remove assets that are joint? When money and property are moved around just prior to a bankruptcy filing it raises eyebrows, at the very least, and can cause further inquiry as to who did what when and why, whose was it and where did it go? (And this is an oversimplification.)
For all of the above reasons, do not allow your fiancee to do this bankruptcy himself. He and you can not afford not to have an experienced bankruptcy attorney guide you through this process. I am not soliciting business because my offices are 3,000 miles away from you. It is simply in your best interest to have an experienced bankruptcy attorney identify issues clearly and advise you as to how to address them BEFORE pen is put to paper in this case.
This answer is provided for informational purposes only. Actual legal advice can only be provided in an office consultation by an attorney licensed in your jurisdiction, with experience in the area of law in which your concern lies.