Scenario: a start-up, post-seed that still has quite a lot of the seed capital in the bank. Investors have lost faith in the start-up's potential, but the co-founders want to keep at it.
The investors would like to split the money left in the bank among themselves and forego their stake in the company. Is there a way for the company to buy back their shares and "erase" them?
Dissolving the company is not a good option because the co-founders wish to retain the IP so that they could continue on their own. Another option is to spin off a new company and sell the IP to it for a penny, then dissolve the old company and let the investors get the money in the bank. However this has some overhead cost (incorporating yet again, new agreements, etc.).
What's the most cost-effective way for a start-up to give up the money left in the bank and return to bootstrapped, investor-less mode without having to dissolve the company?
Yes, a company can buy back its' shares, and this would be a clean and easy way to do this.
Make sure a general offer is circulated to all shareholders, saying the price you are willing to offer, and make sure all shareholders either accept or turn down the offer. This can't be a 'special deal' that only some shareholders get. The ones who don't accept it (founders) should write something on paper showing their refusal.
The fact that it was an open offer, which the investors could accept or turn down, means the investors can't come back to you at a later date. However, make sure that you have communicated everything openly to the investors about the current state of affairs of the company before they make their decision. You don't want them saying you hid information. You may want to consult a lawyer as part of this process (if you don't you are taking a relatively small risk).
P.S. When the company has bought back its' shares it doesn't matter if they are cancelled or held 'in treasury' (owned by the company). You the founders now own 100% of the company, and the fact that the company owns some of its own shares doesn't change your owning 100% of the company that owns those shares.