Less likely conditions

First conditional

In the first conditional, happen to and should can be used in the if-clause to express that something is possible but not very likely:

If you happen to see Kate, say hi from me.
If you should see Kate, say hi from me.

Second conditional

In the second conditional, we can use were to for unlikelihood:

If he were to propose to you now, what would you say?

Third conditional

Here were to + perfect infinitive expresses an imaginary past action which was very unlikely:

If he were to have asked me, I would have said yes.