Is there a word for "becomes empty"?

Andrew Leach is right in saying is emptied is better than empties here.

However, for your particular example, I’d suggest:

During the operation field a is cleared.

When relating to GUIs, it’s a much more common way of expressing that the content has been removed from an input field.

The verb empty can be transitive or intransitive.

[with object] Remove all the contents of (a container)
[no object] (of a place) be vacated by people in it

[ODO]

Thus, the field empties.

Usually, though, where something happens as a result of something else (like a value being taken from a place), the action of an agent is implied by using the passive voice, is emptied.

Another word when used as a verb may be,

Drain

• 1.1 - Cause or allow (liquid) to run off or out of something.
• 2.1 - Cause (a valuable resource) to be lost or used up.

• Example 1: The pond was drained of all the water.
• Example 2: The thief was caught draining all the funds from my account.
• Example 3: Playing football drains my energy quickly.

How about depleted?

During the operation field A is depleted.

MW:

1. to empty of a principal substance. The lake was depleted of water. Depleting the country of its natural resources.
2. to lessen markedly in quantity, content, power, or value. Deplete our life savings. Their depleted resources.