If this problem were addressed

[motico]

"Even if this problem were addressed, the screening of the employees is largely done by [A name of an organization] sympathizers".

Why were and not was?

[Barb_D]

The subjunctive -- though it seems to be dying out. In another 20 years, I expect you'll see more "If it was" instead of "If it were."

[bhaisahab]

"Even if this problem were addressed, the screening of the employees is largely done by [A name of an organization] sympathizers".

Why were and not was?

"Were" is the past subjunctive indicating a hypothetical situation. "Was" is past tense.

[bhaisahab]

?
Even if the situation referred to is set in present or future time, were is still surely past subunctive?

Be is the present subjunctive form.

Yes, indeed.