It's not that there is something missing, per se, it's more like Best regards isn't semantically compatible as the object of the verb in this phrase, we remain. That is, you can't remain best regards, but you can indeed remain yours faithfully.
Your colleague's closing is traditional in form, and rather formal; e.g.,
Assuring you of our best attention, we remain
Here's a modern example from Cybergenix Infotech
Assuring you of our best attention,
We Remain…The more common way to end that kind of closing is as follows:
Assuring you of our best attention at all times / always.
Best regards,Note, regards, if it's the second word of the closing phrase, as it is above, isn't capitalized.