So the rules reference reads

Quote

A ship is jammed if it has at least one jam token. Jam tokens are circular, orange tokens. When a ship becomes jammed, the player whose effect caused the ship to gain the jam token chooses for the ship to either remove one of its green tokens or break one of its locks. If either effect is resolved, it removes the jam token. If the ship does not have any green tokens or is not maintaining any locks, it remains jammed.
After a jammed ship gains a green token or acquires a lock, the jammed ship removes that token or breaks that lock. Then it removes one jam token.

So if I jam a ship with both a focus and a lock, I get to choose which to remove. But what happens if I choose one when the ship only has the other?

Let's say I want to jam "Deathrain" before he moves. He has dropped a bomb, and took the focus action, but I want to prevent him from shooting a Proton torpedo. Can I jam him, choose to break a lock, have him keep the jam token because the effect wasn't resolved and break the lock when he activates and performs an action?

I'd say that doesn't work. That doesn't seem to be what is intended.
However, Jam also states "If the ship does not have any green tokens or is not maintaining any locks, it remains jammed."
Or, not and. So you could maybe argue that yes, if you choose the other thing this works.

However, it seems to me that "You cannot freely choose to do something that is impossible" is a rule running through the whole game. I think this is the intended thing here.

I agree with pretty much everything GermanBlackbot said, except for the interpretation of “or” ... that word is what really forces you to use Jam to remove the green token. W e can simplify the rule to:

J = ( L or T )

If L or T is True, then J is True. The only case where J is False is if both L and T are False.

So no, you can’t “bank” a Jam if at least one condition is met.

Also note that the Jammer gets to choose “you remove a Green Token” or “you remove a Lock.” Not “you remove a Focus” or “you remove the Lock on Iden.” If the target has multiple Locks or multiple Green Tokens, they get to make that secondary decision of which Token or which Lock to remove.

yup if you choose to remove a focus from a ship that only has locks, jam immediately re-evaluates and removes a lock instead.

After a jammed ship gains a green token or acquires a lock, the jammed ship removes that token or breaks that lock. Then it removes one jam token.

You don't get to "choose" a token in general, you choose a token it already has. It would be way more powerful if you could.