"The interest in the LLC (treated as an s-corp) was sold."

You had a sole shareholder. Are you trying to describe that the S Corp is closed down and fell back to an LLC (State construct, single-member = sole proprietorship) existed for the sale? And now they are a partnership; or, still that same EIN S corp? Stock sale = entity did not change.

"The language of the agreement is as follows: The purchasers unconditionally assumes and agrees to pay, perform, discharge and satisfy and and all liabilities of the company. There are no monetary values listed in the contract."

Money in the bank has a stated value, so that part is easy. Fixed and intangible assets would have been valued, too, and agreed upon, and documented.

You likely stated it properly here: "The stock was sold at $24k which is a personal capital gain to the shareholder."

Stop trying to apply anything about the entity to that part of these events. That isn't an internal price or valuation for the entity.

For this: "1) The outgoing shareholder has a negative basis which was classified as shareholder loans in order to balance the balance sheet. The shareholder never made whole on the basis issue."

There will be no "making whole" as it is being forgiven, right? What you seem to have is: the distributions were too high, and would either taxable income each year it happened, or treated as a loan to the shareholder/borrower. They got treated as loan to shareholder, to be repaid? Is there a note payable? If not, then the tax year(s) this happened, it would have been taxable. This assumes it is over and above payroll to that person, as well.

"2) Is the correct treatment for the old shareholder to claim the $135k as income through a 1099C?"

Here's where you start to commingle the perspective. The corporate entity issues a 1099-C, as the lender. This is not a basis issue. Think for a minute if the corporation had made a loan to a unrelated individual. They expected to collect on that loan, so that is an asset to the corporation. Then, the borrower proves to be a deadbeat. The lost asset (the funds) is not basis to the borrower. The unrecoverable asset affects equity, to close out the expectation of repayment. That's what happened at the sale, since everyone agreed the loan is not expected to be repaid, and your borrower is no longer a shareholder, and the event is not a basis event. It's a lending event. At least, as you have described it.

"Does this mean the new shareholders should be able to have an outside basis of $135k"

That's not what they paid. If you buy a $150k house for $15k, your basis is $15k.

"to offset the negative retained earnings?"

As they pay off debt, that will remove the liability. As they operate at a profit, that will increase RE, too.

"Or claim 135k as the sales price"

It's liability. They have the SBA debt. It isn't also part of something else. Go back to my first posting, to see it balances.

"3) How do the new shareholders overcome the negative retained earnings."

Work it, baby!

Someone else will contribute, too, and let me know if I got something not quite right (I'm in a bit of a rush today). Hope this helps.