Can someone get spousal support, if mom is unemployed when the other party decides to leave her and their kids and the unemployment is ending?

Yes.

If you are married, yes, you could receive spousal support since your unemployment is running out.

temporary spousal support is based on the income of both parties, the ability of both parties to work (or not), basically need vs. ability to pay support is balanced between the parties. Permanent support considers those things as well as the standard of living during the marriage and a few other factors.

Spousal support is never guaranteed-there is no automatic entitlement in Washington-but any party to a dissolution action can request it. The court is then supposed to consider all relevant factors including: a) The financial resources of the party seeking maintenance, including separate or community property apportioned to him or her, and his or her ability to meet his or her needs independently, including the extent to which a provision for support of a child living with the party includes a sum for that party; (b) The time necessary to acquire sufficient education or training to enable the party seeking maintenance to find employment appropriate to his or her skill, interests, style of life, and other attendant circumstances; (c) The standard of living established during the marriage or domestic partnership; (d) The duration of the marriage or domestic partnership; (e) The age, physical and emotional condition, and financial obligations of the spouse or domestic partner seeking maintenance; and (f) The ability of the spouse or domestic partner from whom maintenance is sought to meet his or her needs and financial obligations while meeting those of the spouse or domestic partner seeking maintenance. (RCW 26.09.090)

Spousal Support can be on the table if there is a need and ability.

The answer to "can" is clearly yes. The answer to "will a court award spousal support" depends on all the relevant facts. Generally, spousal support involves a question of balancing "need" against "ability to pay".

Possibly

Spousal support is based on a number if factors including length of marriage and marital standard of living. The higher earner pays the lower earner. See an attorney to analyze the factors.

Yes, it is possible, but many unlisted factors come into play.