> The only way to resolve this is i) Gamestop issue more shares/shelf-offering. ii) shorts go bankrupt and/or clearinghouse/brokers take the bill.

No.

You just need one entity, say Blackrock, that is a) long, b) has lent their shares out to short sellers, and c) is willing to reduce their long position (to realise profits, say), then 1 share circulating is enough for the shorts to close their position.

Basically, the shorts can buy a few shares, return them to the whoever they borrowed it from, then buy it again from them, and return it, buy it, etc.

Here's how it works:

1. Initial position

Blackrock long 27 (27 shares), random people long 20 (20 shares)

Note: net share supply = 47

2. Shorter A come in, borrow 26 shares from Blackrock

Blackrock long 27 (1 share, 26 lent to short A), random people long 20 (20 shares), shorter A flat (26 shares, 26 borrowed)

3. Shorter A go short by actually selling to random people

Blackrock long 27 (1 share, 26 lent to short A), random people long 46 (46 shares), shorter A short 26 (0 shares, 26 borrowed)

4. Shorter B come in, borrow 45 shares from random people

Blackrock long 27 (1 share, 26 lent to short A), random people long 46 (1 shares, 45 lent to short B), shorter A short 26 (0 shares, 26 borrowed), shorter B flat (45 shares, 45 borrowed)

5. Shorter B actually go short by selling 45 shares to redditors

Blackrock long 27 (1 share, 26 lent to short A), random people long 46 (1 shares, 45 lent to short B), shorter A short 26 (0 shares, 26 borrowed), shorter B short 45 (0 shares, 45 borrowed), Redditors long 45 (45 shares)

Note: longs 27 + 46 + 45 = 118, shorts 26 + 45 = 71, net 118 - 71 = 47

And, redditors with their 45 shares won't sell, and won't lend.

You say: > The only way to resolve this is i) Gamestop issue more shares/shelf-offering. ii) shorts go bankrupt and/or clearinghouse/brokers take the bill.

I suggest:

There is one random guy that still has a share (all the others have lent them out). So:

6. Shorter B buy a share from that random person with a share (they're happy to sell it at this high price):

Blackrock long 27 (1 share, 26 lent to short A), random people long 45 (0 shares, 45 lent to short B), shorter A short 26 (0 shares, 26 borrowed), shorter B short 44 (1 share, 45 borrowed), Redditors long 45 (45 shares)

7. Shorter B return the 1 share to the random person they've borrowed it from:

Blackrock long 27 (1 share, 26 lent to short A), random people long 45 (1 shares, 44 lent to short B), shorter A short 26 (0 shares, 26 borrowed), shorter B short 44 (0 share, 44 borrowed), Redditors long 45 (45 shares)

8. Shorter B buys the 1 share from the random person they've just returned it to:

Blackrock long 27 (1 share, 26 lent to short A), random people long 44 (0 shares, 44 lent to short B), shorter A short 26 (0 shares, 26 borrowed), shorter B short 43 (1 share, 44 borrowed), Redditors long 45 (45 shares)

9. Now, return steps 7+8 43 times:

Blackrock long 27 (1 share, 26 lent to short A), random people long 1 (0 shares, 1 lent to short B), shorter A short 26 (0 shares, 26 borrowed), shorter B short 0 (1 share, 1 borrowed), Redditors long 45 (45 shares)

10. And have short B return the final share to random person. Then shorter B is flat, and out.

Blackrock long 27 (1 share, 26 lent to short A), random people long 1 (1 shares, 0 lent to short B), shorter A short 26 (0 shares, 26 borrowed), Redditors long 45 (45 shares)

11. Now, have shorter A to the same game with 1 share from Blackrock 26 times - Blackrock is probably also happy to sell at these prices:

Blackrock long 1 (1 share, 0 lent to short A), random people long 1 (1 shares, 0 lent to short B), shorter A flat (0 shares, 0 borrowed), Redditors long 45 (45 shares)

12. Endgame.

Shorters are out, despite the fact that redditors were holding 45 out of 47 shares, and never let go of them!

Blackrock and random people have reduced their long exposure to 1 each. Redditors are stuck with 45 shares.

Note: how much the shorters lost depends: they sold in step 3 and 5, and bought back in steps 6,8,9,11. The price difference determines their loss. They probably lost quite a bit. Blackrock and random people probably won quite a bit. Redditors that are left with the 45 shares... depends for what price they can sell it.