My dad had an annuity, no beneficiary, is it possible that I get no money from it, even after taxes and fees. Like could the annuity company/state just take the money?

Even if your father has not designated a beneficiary for his annuity, the annuity account holder or the state cannot "take" the money.

When a person dies intestate, or without a will, the laws of the state where he resided determine how his estate is distributed. According to these laws, specific family members, or heirs, have a right to inherit a share of the decedent's property.

It's possible for an annuity to have no death benefit.  It depends on the annuity contract.

If the annuity does have a death benefit and the annuity has no designated beneficiary, the death benefit distribution will be made to the default beneficiary indicated in the annuity contract.