If documents are stored in the cloud is this safe?
By default it is stored on your hard drive, but you can chose to store your documents in the cloud, or send it to a server by FTP, etc…
If you want to see by yourself, open Writer, type the letter a(to write something) then Ctrl+s (to save it) or in the top menu File then select Save or Save As... or Save a Copy or Save All or Export or Export as PDF, you will see a window opening and asking you where you want to save the document on YOUR HARD DRIVE.
You can also save your documents in the Cloud via the top menu File then select Save Remote... then a window will open, click Add Service a new window will open where Google Drive is selected by default (input your login and password). You can click on the Google Drive in this same window to see all the cloud services LibreOffice as set by default if you do not want to use Google Drive.
If documents are stored in the cloud is this safe? It is all about your point of view, and what you call safe. For this question you might need to ask on some specialized websites about cloud services safety and availability of such a service
EDIT IMPORTANT about cloud services in LO: I would like to point out that there are know bugs about cloud services which are not yet resolved like with Google Drive (the 2 factor identification) and other cloud services in LO, please read the comment section of this answer to know more about it and some possible work around depending your OS.
Remote services such as One Drive and Google drive have not worked within LO for some time. There are outstanding bug reports on these.
@Ratslinger,
Because of your comment i just discovered the bug (thanks a LOT), I discovered also that it is not working depending your username on your google drive account and it will shows up a 2 identification factor (input a 6 digit that google should send by sms, so i tried it, but I did not receive the 6 digit via SMS…
In this post LibreOffice access to Google Drive asks for authentication 6-digit pin
@libusr is speaking about a work around and he said: You must have access to your Google Drive from within your computer’s directory system (I suppose like the Dropbox).
If you have, then you can ignore the seeming non-functionality of ‘Save Remote’ and instead simply select ‘Save As’ and locate the Google Drive directory as the destination for your saved file (which should sync with your online account).
Anyway there many cloud services to chose from on LO 
Two factor authentication always shows in LO even with it turned off in Google. This is part of that bug. You will not get a code from Google.
Point is, even though you can use other software in your OS for cloud access, these services don’t work within LO.
In Linux, for example, you can also use Gnome accounts to access Google Drive.