CPA specializing in cryptocurrency taxation here. The missing 1099 from a defunct exchange is a scenario I deal with regularly, especially after the collapse of FTX and several smaller platforms. Here is the practical approach I use with my clients.
First and most important: you are still required to report your crypto transactions regardless of whether you receive a 1099. The IRS has made this abundantly clear in their FAQ on virtual currency and in Notice 2014-21. The obligation to report lies with the taxpayer, not the exchange. A missing 1099 is not a defense to underreporting income.
Regarding cost basis: if you truly cannot determine what you paid for the crypto, the IRS does not allow you to simply use zero basis (which would maximize your gain). Instead, apply the best available evidence -- market prices on the dates of acquisition, average cost basis from the exchange period, or comparable transaction data. Some crypto tax software platforms have built-in tools for estimating basis from defunct exchanges using historical price data.