Fighting for it would be extremely inappropriate in most circumstances. There is a lot of decision-making and considerations going into evaluating employees. Friend (for simplicity "Alice") saying "you were wrong to let me go, fire other employee (for simplicity Bob) instead!" would not go down well. It comes off as arrogant and petulant. Even if rooted in good intentions and correct information. However, it might not be:
- Bob might be the boss' nephew. Yes, nepotism exists - fighting to get them removed will not work.
- Bob might have legal reason to be retained. In that it might be extremely risky to let them go.
- Bob might be contributing in ways less visible - both visible in stand-up or otherwise.
- Bob might have a family and kids, while Alice is single and childless. A boss might be less inclined to lay off a family person. While single are viewed as more financially independent. This is a human factor consideration.
- Alice might have shown to be undesirable to work with despite their high contributions. Thus it is not contribution to project which was a deciding factor.
- Alice might be good employee, has even done excellent work. However, maybe that work is no longer needed, thus no reason to retain them. While the Bob does some tasks that are still valuable. Pure financial decision.
- Bob might saved the boss' prize pet hamster from a burning building, now the boss feels retaining a job is the least reward. Is it likely? Probably no. Point is there can be many other considerations.
There is nothing to gain here that will not come at the cost of goodwill. Best case scenario is:
Alice is reinstated, Bob let go instead.
However: Now lots of the other employees would know Alice as "the one who got Bob fired". Even if that was an overall good decision (Bob was indeed lower valued employee, Alice was indeed a higher valued one), it would what could be perceived as mud slinging.
Even a neutral does not work that great:
Alice remains laid off, Bob remains employed.
However: Alice is still coming in a bad light trying to get somebody else fired.
Even worse for Alice would be the case where Alice remains laid off, Bob also gets laid off.
All possible result that will come up accompanied with the airing of dirty laundry. That will involve Bob's but also very likely Alice's.
The quote from War Games rings true:
A strange game. The only winning move is not to play.
Even a more fundamental issue here is understanding that a business is not a friend or family. Once the contract is finished, Alice does not owe the ex-employer anything. And vice versa. The social norms would be to keep in touch with ex-colleagues you got along with. Maybe even provide small helpful information to the company. In general, mildly amicable relationship, if any.
Either party trying to besmirch the other is not acceptable.
Even if Bob is really dragging the company down, even if Alice was a key employee to keep it up. Even iff the decision for who to lay off or not right now directly leads to the company's downfall. Were all of this unequivocally true, Alice does not need to do anything here. The company's success is not Alice's direct concern any more. Not any more than anybody else who is not an employee.
Worth noting that it is rather unlikely the fate of the company to be resting at Alice's shoulders anyway.
With all that said, if Alice was indeed as a good employee as described here, they should have little trouble finding another job. They should concentrate on that. In general, spending time and energy on previous employers when there was contentious circumstances is not a useful endeavour.