Based on the scripture you cite and your situations, I think it is obvious that being abandoned means the covenant was broken by the other spouse.
A covenant is a sort of a contract. When broken by the other party, the offendended party is released from it and is free to remarry.
—When broken by the other party, the offendended party is released from it and is free to remarry.—
In our culture, we call that a “divorce” and Jesus uses that word. Are we dealing with a situation where our culture’s meaning of the word is different than the culture of Jesus day. I understand he is speaking to Jews in a pre-Christian world. Maybe I need to research this more.