Other platforms may be different, but with BD’s Diva software you can only collect one “unstained” compensation control, so if it is necessary to mix what type of compensation particle you are using (cells for PI or DAPI, Arc beads for Live/Dead amine reactive dyes, rat comp bead or mouse comp bead for antibody from rat or mouse) you would have to define a different negative population for each type to get proper compensation. In Diva, this is done by having an internal negative in the data file, and drawing a new interval gate on the histogram for that single stained control. In the absence of this additional gate, the software refers to the “unstained control” tube for the comparison.
At certain points in manufacturing, companies must change the batch of plastic they use for their bead, and the new batch can have different fluorescence properties in some channels, especially in the 450nm emission range with 405 excitation (the “Pacific Blue” channel). If you mix your lot numbers of beads, you may get a mismatch. In this plot an older vial of “non-binding” bead is mixed with a newer vial (later expiration date) of unstained binding bead and you can clearly see the difference in intensity:
When you add an antibody to this mix which is known to have no spillover into Pacific Blue (such as PerCP-Cy5.5) you still see a separation in the populations. The software is going to look at the positive population (green) and compare the mean signal for that population to the mean signal of the negative population (blue) in Pacific Blue, and since the positive is higher, this difference is attributed to spectral overlap and a compensation value is determined even though there is no fluorescence spillover, it is just a difference in the plastic.
If compensation is calculated in this case, any time you have PerCP-Cy5.5+ events, there will be signal inappropriately subtracted from the Pacific Blue channel. On the left is the wrong compensation, on the right is compensation calculated with properly-matched beads.

This was a 4 color experiement so the error was easy to notice, but in more complex panels this will not be the case, so make sure you do it right from the start!
I posted to on the Purdue message board about this a while back, here is the link towards the end of the thread with the previous messages attached, start at the bottom to go through the discussion chronologically.
https://lists.purdue.edu/pipermail/cytometry/2011-April/041298.html