As iMAGEbox suggested in a comment, this can happen when someone else gets the kill-blow on a dragon in the same cell (which might actually be out of your line of sight, and happens pretty often in city attacks when a dragon isn't in the mood to land near you).
Another cause of this is killing a dragon while there's a big backlog of Papyrus script-processing. On a "potato" PC (or one that's better but running a huge pile of mods, or with other processes chewing up CPU cycles and RAM; or if you're playing in a VM on Mac or Linux), the game's script processing can get bogged down, and actions/reactions that depend on script completion can be deferred (or even fail if they have timers in them, or depend on Script A completing before Script B will do what it's supposed to).
A common symptom (aside from crashing every few minutes), and thus an easy test, is Soul Trap seeming to not work, until minutes later (sometimes quite a few minutes) and then you get a whole bunch of captured-soul sound effects and messages seemingly "out of nowhere" as the game catches up. This can also happen with a dragon kill and the specially scripted dragon-soul absorption routine. You can be half way across the map from where the kill actually happened when the script finally completes.
There can be other weird symptoms, like loss or distortion of sound effects, scripted NPC and quest actions not happening (this is the most serious consequence), stuttering of animation and sound, followers not following you through a cell change, ash piles appearing for no reason (especially ones that cause a CTD when you try to open them or even
disable them with the Console), hotkeys added by mods not working when you press them, etc., etc. Basically, if the game is badly freaking out, script lag is likely the cause.
The short-term fix for this is to go somewhere safe with little happening or likely to happen, and just stand around idly, saving every minute or so (especially after evidence of some delayed script completing) until you don't get any more indications that scripts are still waiting for their turn, and the game does seem to be back to normal. If you want to be certain, have empty soul gems in inventory, then go soul-trap and kill the first bit of wildlife you encounter. If you capture the soul on the spot, then you're good to go. Also, if the game crashes during your wait-it-out phase and crashes again when you try to load your most recent save, try loading a much older save that was saved in a calm place like a shop, then load the most recent save.
Another quasi-fix is to just revert back to an earlier save that doesn't seem to be having this script-lag, then re-play through whatever you were doing before the problem started, but do it more slowly. Speed-running and doing anything script-intensive aren't a good combination.
Long-term, you need a higher-end PC, or the script lag will continue to happen periodically.