What happens if the power fails during a write/erase cycle on the eMMC?
As most of the storage, the data which is being written may not written completely and so dataloss can hapen
In the anticle Preventing Filesystem Corruption in Embedded Linux I read about “Data Reliability Mode”, is this supported by Colibri iMX6?
Yes, this mode is supported by the used eMMC Flash for Colibri iMX6.
Is there any hardware method, a capacitor or something, to prevent a power failure during a write/erase cycle?
No, there is no capacitor the module to keep energy for eMMC in case of PowerFail. This PowerFail Proection Mechanism has to be placed on the carrier board.