I haven’t seen much about this on the web, but with our two older machines (MacBook Pro 2010 and iMac 2009), we have had hang problems with File Vault. On the former, the upgrade just failed and hung at a blank screen. The on the later, it worked, but then on some update, it would just turn off after the login was accepted. Even going to single user mode didn’t help. I think the problem is that the disk is locked and there is some sort of bug where El Capitan cannot open it.
The only fix I could find (after trying recovery mode, single user mode, disk utility repair) was a total reformat and rebuild. So you are warned

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