To pick up where Forest left off with this one - Malwarebytes will move the suspected/infected file from its current location and then store it in a new location they call a "protected container" e.g quarantine. It is stored in such a way that the file can no longer be executed, this is typically done through the method Forest described. 
MB has a "dumping" feature if you dump a file in the quarantined items then it will no longer be at all restorable and you would have to re-install if you wanted the file back as once you dump it, it's completely destroyed. All files from the quarantine can be moved back to your system if you wish, just not dumped files.
In regards to your second question, no it wouldn't be possible. A quarantine is a separate file location that MB will move the files to, I tried Googling for any kind of case in which a virus made itself appear to be moved into the quarantine location, however, I couldn't find anything. The problem here is once the file is moved there, it cannot be used it has to be taken back out of the location for the file to be executable again.
1 - I had a look on the specifics of how Malwarebytes obfuscates their quarantined files, however, I couldn't find any resources or comments on it.