As long as the stock is sitting in your demat account with CDSL/NSDL, it doesn’t matter which broker you are using and even if a certain broker goes down, it won’t affect your stocks in demat as it is maintained by CDSL/NSDL.
How safe it is to trade with Zerodha, I had answered this long back here. All the reasons hold true even today after almost 3 years. Today there are over 250,000 clients who would probably vouch for the same.