I assume that HUSBAND is the decedent or that you are asking what happens on HUSBAND's death. In answer to your question, the language you quoted is language that would be found in a pour-over will. It does cover assets of the type you state held in HUSBAND's name alone (your fact) as long as there is no pay on death beneficiary.
I recommend that you speak with an attorney to assist you with the probate, if one is required. Depending on the value of the assets, they may be able to be collected by an affidavit.
DISCLAIMER: THE INFORMATION PRESENTED HERE IS GENERAL IN NATURE. IT IS NOT INTENDED, NOR SHOULD IT BE CONSTRUED, AS LEGAL ADVICE. THIS RESPONSE DOES NOT CREATE AN ATTORNEY-CLIENT RELATIONSHIP BETWEEN US. YOU SHOULD CONSULT WITH A QUALIFIED ATTORNEY FOR SPECIFIC LEGAL ADVICE ABOUT YOUR PARTICULAR SITUATION.
I agree that this would normally be language that would be included in a Will. I am concerned that this language is NOT in the Will, however, and might be included in the trust. If that is the case, you will not be able to avoid probate for these assets, and if there is not a Will that has this kind of provision in it, then the assets will not be transferred to the trust and will not go to the beneficiaries that are supposed to receive them.
If you are trying to avoid probate, then you need to actually transfer title to the trust or set things up in such a way that title otherwise passes automatically upon death to the trust or beneficiaries. Otherwise, probate will be required.
If this was not set up by an attorney, it should have been. I would take all of the documents to an estate planning attorney and have them reviewed to make sure what exactly you have, and what, if anything needs to be done. If your husband is already deceased, then it may be too late to make any changes to HIS estate plan. The effect of what he has is something you would need to address with the attorney.
*** LEGAL DISCLAIMER I am licensed to practice law in the State of Michigan and have offices in Wayne and Ingham Counties. My practice is focused in the areas of estate planning and probate administration. I am ethically required to state that the above answer does not create an attorney/client relationship. These responses should be considered general legal education and are intended to provide general information about the question asked. Frequently, the question does not include important facts that, if known, could significantly change the answer. Information provided on this site should not be used as a substitute for competent legal advice from a licensed attorney that practices in your state. The law changes frequently and varies from state to state. If I refer to your state's laws, you should not rely on what I say; I just did a quick Internet search and found something that looked relevant that I hoped you would find helpful. You should verify and confirm any information provided with an attorney licensed in your state.
I would agree that the standard clause in a pour over will would include all assets in just the name of husband and would in effect be left to the wife as owner of everything in the joint trust.
The answer given does not imply that an attorney-client relationship has been established and your best course of action is to have legal representation in this matter.