Proof of stake fork problem I have a doubt with Proof of Stake. As I have watched some tutorial videos and websites, there is information that: with Proof of Stake, in order to make a double spending attack, a node has to own at least 51% stake of all the network.

Because with pure Proof of Stake, only a single miner can append a block at the same time. So what I wonder here is: with Proof of Stake, how can fork happen to make the double spending attack? 

Thanks in advance :-)
a node has to own at least 51% stake of all the network.


This is correct. Note: you should own 51% of network, not 51% of emission.


  only a single miner can append a block at the same time


Not true, but it does not matter.


  how can fork happen to make the double spending attack?


Assume you have large stack. 


backup your database at some checkpoint 
sell your stack for "anything else"
restore from backup and create a private network which is not connected to main network
leave your chain mining until the cumulative difficulty become larger than in main network
connect your network to main net and force it to reorganize mainchain to your chain where you still have your funds and 100% mining rewards


voila