In theory, yes, the PAF can pursue used F-16s. Pakistan is (on paper) a Major Non-NATO Ally (MNNA) and can request access to mothballed ex-US equipment, and only pay for refurbishing them (under the Excess Defence Articles) program.
But when it comes to Pakistan, the theory doesn't apply.
The US isn't in the mood to help Pakistan get militarily stronger (as that'd concern India, which the US is working to get on board to help contain China).
The US wants normalization of ties between India and Pakistan (read: for India to get what it wants so that it can focus on China ... aka de-fang Pakistan).
The US is not going to de-fang Pakistan, but it doesn't want to sharpen those fangs either -- unless now India becomes a threat to the US.
That latter issue is at play from a policy standpoint, which has made getting used US equipment difficult for Pakistan. It's not just the F-16s, but also old helicopters, C-130s, old frigates, etc, you name it.
TLDR: The PAF is on everyone's sh!t list, more so than even the Pak Army or Pak Navy. Basically, air power is a strategic asset, especially if you have offensively capable assets and the freedom to equip, configure and deploy them at will.
And Pakistan is currently in a situation where it is an indirect threat to US interests (i.e., diverting India's attention away from China). The US will deny us that asset.
So, the only way to break from that is to (1) structurally transform your economy and get a miracle in your name so that you can outspend India on defence and/or (2) get solutions of your own like Project AZM.