Well it depends on the file system.
Let's see what happens in the hardware area.
Without a proper shutdown, the memory DIMM's is not refreshed as it ought to do, and without a constant refresh, it will loose data. Without that in mind, what happens is that the data will be replaced with static or garbage.
The hard drives will run a bit longer than the dual in-line memory module so if it is written onto your computer disk, so the direct memory access controller will keep running and will write the "garbage" fed by the DIMM, so it will keep reading but what it's reading is corrupted data. The DMA will keep reading data from memory, but it has no idea that this data is corrupted.
Although the entire file won't be corrupted, some of it will be due to the decrease the refresh cycle of your RAM, it is apparent that some corruption still occurs.
The chance of data loss increases in a power failure when you are using an encrypted file system.
If your hardrive is old, added to the corrupted data, there is a chance you'll break it, so next time you try to boot up, it won't.