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.
The drop in incentive to secure the network with increase in mining to the point where most of the 21M supply of BTC is a real challenge.
Right now, miners mine because they are incentivised to do so by receiving rewards with every mined block but as that community becomes smaller and smaller, people would probably take a different angle to security because then there's no point in holding a very scarce assets like BTC if it's not valuable due to next to no security. Which groups will take that approach if security doesn't become obsolete in the next 100+ years is something I can't even start guessing as most people today will not be around then, and technology can take us much further in a century.
Interesting debate, nonetheless...