The short answer is yes.
Since your mother was alive when your Aunt died, the inheritance vested in her. As result of that, there is money which would be subject to a Medicaid Lien.
Yes in all likelihood. The only exception is if Mom's S/I/L had a provision (common) that said a beneficiary had to survive at least [e.g., 30, 60, 90] days after the testator's death in order to collect.
So -- if S/I/L had such a clause in her will (a question?) then your Mom's estate may not be entitled to anything at all if she died in the designated window period (if any) as I gave by example.
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.
If I understand your question, your mother survived her sister-in-law and became entitled to a share of the sister-in-law's estate, which at the time of her death had no assets, but subsequently (4 months later) received cash. Later, your mother passed away.
It is unclear whether you are concerned about Medicaid making a claim against your mother's estate or the sister-in-law's estate. But regardless of which estate we are discussing, Medicaid can make a claim against probate estates and if the estate has funds, then Medicaid may be entitled to some portion of those funds. The fact that the estate had no funds at the time of death does not make any difference here. Nor does it make any difference whether the sister-in-law knew or didn't know about funds possibly coming to her in the future.
There are provisions to avoid a Medicaid claim if there is a hardship will be created by the claim. However, such hardship claims are only available for limited situations.
It is impossible to give specific answers to questions without meeting and fully discussing all of the potential issues that may not be addressed by your question. The answer(s) provided should be considered general information and are not legal advice. Viewing this information is not intended to create, and does not constitute, an attorney-client relationship. The answer provided is intended to educate you and point to issues for you to raise in a consultation with a lawyer. You should not take any action that might affect your claim(s) without first seeking the professional opinion of a licensed attorney.