This reminds me of a senior project manager who told that he knew the team could not meet its next deadline but he kept it secret in order not to kill their motivation.

Apparently he thought the team would not notice that their velocity was too low or that maybe if he didn't do anything they would work faster...

Unfortunately this kind of behaviour is all too common.

Project management is all about getting the truth out there in the open - making everything transparent and working to solve the problem. Hiding the bad news and painting a sunny picture is not management. It is sabotage.

In a situation like the one above the proper response is to say, OK we are not going to make it and then MANAGE the situation - merely working overtime does not truly solve the problems. It is more like driving on the motorway in the second gear and spending more time on the road rather than switching to a higher gear.

You have to solve the problem at its root cause.  If the velocity in a software project is too low it is probably because the quality of the system is too low. It could be that the architecture needs to be fixed (refactoring) or that the team is putting too much effort into coding bugs into the application. In the latter case it would probably be wise to teach the team how to stop the bugs from sneaking in rather than letting bugs into the code base and spending a lot of effort later to find and remove them later.