I believe we just experienced this with Kitty last night.
His evening preshot was 26.1 mmol/dl, quite high. I gave him his full dose. Note that when I report a result, I report it as the amount of time after his shot. Therefore, preshot is before he gets his shot. +5 is 5 hours after his shot, etc. At +5 he was at 3.2, which is a HUGE drop from his preshot. At +6, he was at 4.2, so I felt he wasn't going to go any lower and I went to bed.
This morning, his preshot was 21.6, which isn't too bad considering the huge drop he had last night. However, it all went down hill from there, until +7 where I actually got a reading of HI on the glucometer, meaning he was over 33.3 mmol/dl.

Not a good day. Hopefully tomorrow will be better.