The short answer is, yes. Even if it does not, you might loose all your bitcoins.
Every bitcoin wallet address comes with an address and a private key. The private key is required for using or sending the bitcoins held within the wallet.
Technically, Zebpay is your online bitcoin wallet. Hence it holds your wallet address along with its private key. If someone from Zebpay got corrupted enough, he could easily flee away with as many private keys (and address pairs) as he can. Also, if hackers got hold of the private keys by some means, Zebpay could do nothing about it and yet they would be blamed. The end result would be that you will be at loss.
The cheapest and best way to deal with all this is to have an offline paper wallet. To do that go to bitaddress . Once the page loads, disconnect from the internet (for additional safety). follow the instructions and generate a bitcoin wallet address with private key. Take a print of it and store it safely in secure locker! Now feel free to store many bitcoins in this address. I personally prefer to store the digital copies of paper wallet by adding password protections to those files.
I have been investing and mining bitcoin since it was around 50K INR. I have online wallets with Unocoin and Zebpay. I have multiple paper wallets which I have safely stored somewhere. Most of the amount I buy on either of the exchanges goes to my paper wallets. This keeps my bitcoins secure from whether Zebpay is hacked or whether they run away.
This also applies to other similar online wallets like Unocoin.
Bonus tip: Incase RBI/Govt decides to make bitcoins illegal in India, Zebpay would be forced to shut down. You might be forced to sell off your bitcoins or may end up losing them unless you have stored them securely elsewhere.
Update: Since many of you asked how to transfer BTC from paper wallet to elsewhere, I use Bitcoin Block Explorer - Blockchain to do that. There you can import your paper wallet as well as the private key and send the required amount of bitcoins. Whenever I do so, I create another paper wallet and transfer the remaining coins there, merely for safety.
Update 2: Since some of you wanted to know about creating a paperwallet. I have created this post: How to create a bitcoin paper wallet (cold storage)
Update 3: Since some of you wanted to know the exact steps to withdraw bitcoins from Zebpay to your paper wallet, I have created this post: How to move bitcoins from Zebpay to your paper wallet
Note Originally, this was my answer to a question on Quora, but due to certain moderation policies on Quora, they deleted the answer. I had to edit the answer to post it on Quora. The complete answer has been posted here.
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