It is quite possible for a power failure to create an error in any part of
the disk. For instance, if the FAT is being updated at the moment of
shutdown then a whole sector of FAT data, involving many files, can be
corrupted. In the wort case, power failures can damage hardware, as they are
often accompanied by spikes or brownouts. The typical PC power supply is
actually very good at filtering these effects, but it can happen that
components are damaged.

It is unlikely that anything other than open files (or such items as the
FSInfoSector) will be affected by switching the machine off, provided there
is no active disk process occurring at the time. Note that any open file,
not just a file currently being written to, is at risk.  Note also that
different file types have different risks - a simple text file being
processed in a text editor is probably unaffected by an illegal shutdown,
while a database file can be corrupted beyond repair.

A cross-linked file is usually a symptom of data loss, not a cause - data
from one file has been written over the top of another file. The error
becomes visible when the FAT checking reveals the cross linking.  It occurs
because of an error in the FAT, where a sector that is in use is processed
as if it were free, and is allocated to a new file. The data from the latest
file to use the sector is usually recoverable, while the previous data has
been overwritten and lost.  Cross linking should not occur if the FAT is
repaired on the next start-up following an illegal shutdown, but of course
the data may have already been lost..