Important subject; I had never thought of this.
Watching.
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?
I guess you mean that miners' incentive will become less and less overtime. Yeah, that might be true. If we assume that it will be globally adopted in the future and that its price will be less fluctuating, then each halving will simply make miners' profit halved, which means less computational power offered into the network and hence, less security.
I'm curious why this thread hasn't been filled with anxious replies and counter-arguments yet.