You can

a) reveal sleepers in your system(s), if you unlock this tech -> Mineral Manipulation

and

b) kill sleepers in your system(s), if you unlock this tech -> Optimized Logistics

No "healing" possible.

Of course if you have a crappy spare system lying around, you could just send known sleeper pops to that system so the enemy gets no useful info or resources from them...

Groo wrote:

You can

a) reveal sleepers in your system(s), if you unlock this tech -> Mineral Manipulation

and

b) kill sleepers in your system(s), if you unlock this tech -> Optimized Logistics

You can unlock Optimized logistics to kill them,

Sublustris wrote:

In your system tab to the left there is a button under Domestic surveillance block: Sleeper reintegration. After acivating it, it will lover your system happiness by 25% (it will consume Keii for Hissho) for 5 turns, but will revert 1 sleeper on 5th, if any are present. If there is, action will proceed for another 5 turns. If there is none, it will alert you that there is none and cease to work.

or to "heal" them you use this.. Just one note I think the turns that takes to revert one sleeper depends on the game speed. I think at normal is 10 turns.

So healing it is possible but it is pretty slow.

Sleeper reintegration(aka healing Sleepers) takes 5 turns on normal speed. Can't say what it is for faster game speeds or on Endless game speed. When reintegrating, system happiness/loyalty takes a 25% penalty(Hissho consumes Kei) and every 5 turns a Sleeper is "healed" or removed from play and continues for another 5 turns until all Sleepers are healed/removed. Researching Mineral Manipulation allows you to verify that there are sleepers(as opposed to a backdoor or some other hacking option) while Optimized Logistics allows you to instantly kill all Sleepers on a system. I often grab Mineral Manipulation not just for the reveal function but also for the +5 Dust/pop on Sterile planets.