Conceptual question on Pareto Optimality: Are one-way transfers valid “trades”, and does PO always guarantee mutual exchange?

I am analyzing a 2-person, 2-good Edgeworth box economy where one individual has Leontief preferences and the other has linear preferences, and I ran into a conceptual roadblock regarding the strict definition of "trade" vs. "Pareto improvement."

The Setup:
* Person 1 Preferences: U1 = X1 + Y1
* Person 2 Preferences: U2 = min(X2, Y2)

Because Person 2 has Leontief preferences, any allocation off their "kink line" means they hold an excess of one good that provides them with exactly 0 marginal utility.

The Scenario:
Suppose we are at an allocation where Person 2 has excess Y (so Y2 > X2). Those extra units of Y are essentially "worthless" to them. If Person 2 were to simply give this excess Y to Person 1 for absolutely nothing in return, Person 1's utility would increase, and Person 2's utility would remain exactly the same.

My Questions:

1. One-Way Transfers: Colloquially, "trade" implies a mutual exchange where both parties give and receive. In general equilibrium theory, is a completely one-sided transfer (giving away a good with zero marginal utility for free) allowed to be considered a Pareto improvement? If so, does this strictly rule out any points off the Leontief kink line from being part of the Pareto optimal contract curve?

2. The Definition of "Trade" vs. "Optimality": If I explicitly define a "trade" strictly as a scenario where both parties must receive something in a two-person world, when does Pareto optimality fail to guarantee that such a trade exists? Put another way, are there standard economic scenarios where the only path to the Pareto optimal set requires these one-sided "gifts" rather than mutually compensated exchanges?

Would appreciate any insights from a rigorous micro theory perspective!