If you have a flash drive full of bitcoins and then suddenly, you lose it or it became unusable, the bitcoins in there will be gone forever. Am I right?
It's not that Bitcoin's are gone forever, but more so that you can't access them anymore.
So, if that's the issue, is it possibe that we run out of supply of bitcoins?
Only a very small number of coins are not accessible anymore, which isn't something that will play a significant role in the future. The higher the price is, the lower the amounts are that people can afford to buy. People at some point will transact with Satoshis in the distant future if Bitcoin lives up to what people expect from it. In other words, plenty enough Satoshis for everyone.
If that were to happen, will bitcoin die along with other coins? Or will it die alone?
No and No. To add; altcoins do not depend solely on Bitcoin anymore. Most of the top altcoins have their own fiat trading pairs, and in case Bitcoin isn't there anymore for whatever reason, another altcoin will replace Bitcoin and become the main benchmark coin.