Minimum allowable gas fee (Gwei) under EIP-1559

Curious, what happens these days if you send a transaction that uses a super low Gwei value … let's say Metamask suggests at least 40 Gwei but you manually overwrite it with 10 Gwei. (And 10 Gwei would be below the EIP-1559 base fee.)

Would this TX remain in the mempool until eventually (maybe weeks later) someone mines it, or would it simply fail? If the latter, how quickly would it typically fail?

For context, in other chains it's quite common that people just send a TX using the minimum allowable fee (e.g., 1 sat/vbyte in BTC) if they don't care how long it will take. In most cases these TXNs will confirm at some point.