When Bitcoin gets to a stage where the mined supply is basically 21m (that is, very little remaining btc left to be mined), will Bitcoin still remain a secure network?
If you mean that miners will not be interested in providing us with security and network,I think that they will still be interested in it. To my mind, when Bitcoin reaches its max total supply, miners will get just our commissions for running our transactions, but not new bitcoins as they do now. So there will still be people who want to be miners. To sum up, we shouldn’t be scared.
Miners will keep on mining as they can still make a decent commission in the market. Despite the huge expenses that they take every day but I think they are still at good and profiting from mining and that is why many keep their job.
But this is not what the OP has meant, he just thinks and doubted what will happen if the total market supply of Bitcoin will be mined? But I don't think this could wipe out the security we have and I have no doubt about that. As we are using blockchain technology no matter if we all mined the 21m, there is no reason why it makes Bitcoin unsecured.