Is it possible for a STOP LOSS set to fail to withdraw when it reaches the amount set?
Did you mean if stop loss can fail to trigger when the stop loss price is reached? Yes, but it is not common. It happened when the crypto market is extremely volatile.
You are correct @ Charles-Tim. High volatility can course that to happen. I would even say we might have experienced that earlier this year, maybe around May that there was crypto crash or something that caused some trader's taking there lives because of the loss they encountered, I feel some would have used SL yet, they weren't saved. Again, I think I have witnessed that too in FX when a very high impact news is released like unemployment rate, non farm payroll.
Is there anything as STOP PROFIT in trading that can be set to automatically withdraw investment when profits reaches a particular point where it's set to stop?
It is called TAKE PROFIT, TP for abbreviation. It doesn't withdraw profit but lock it up for you by closing your trade in profit when it gets to the point you set it. It is very useful and nice to be used because while you are not there present, it helps you take the profit that you have made instead of losing it back to the market. I would say it is the opposite of SL.
There is another feature of TP, it is called trailing stop. It takes profit for you in little little profit or pips as you set it. So, yes there is Take profit.