That only works if we're operating below our accruable space limit after the player is placed on LTIR. It has to do with the difference between the Salary Cap Limit and the Accruable Cap Space Limit. LTIR raises our Salary Cap Limit, but not our Accruable Cap Space Limit. For most teams, that's the same number - 81.5 million in 20-21. But for teams who place players on LTIR, their Salary Cap Limit is raised to 81.5+whatever that player costs, but the Accruable Cap Space Limit doesn't change. It's still 81.5. Whatever we operate below that we accrue.
For example, using the team above that has Tarasenko on LTIR, our Salary Cap Limit now goes up to 89 million. As long as he is on LTIR, we are allowed to spend up to 89 million dollars (including him) on our roster. BUT, our accruable cap space limit doesn't change- it's still 81.5 million. If we are operating below 81.5 million after Tarasenko is on LTIR, then we will accrue cap space. But for this team in particular, that is spending a little over 87.5 million on its roster, we're operating above our Accruable Cap Space Limit. This is fine, since we're still below the 89 million Salary Cap Limit, but it means we won't accrue cap space throughout the year for a rental or something.
This is a big reason why we didn't immediately try to replace Tarasenko last year when he went down- we would have been able to land a high salaried rental with our accrued cap space at the deadline and still been able to bring Tarasenko back if he came back before the end of the season (which was looking likely before the pause).
If the above roster were to happen, we would have to clear nearly six million in cap space to allow for Tarasenko to come back when he's healed, since we won't have been accruing cap space throughout the year.