is possible some elements absorb neutrons, without any nuclear reaction?

Well, the capture rate would be related to the cross-section - if you surround a neutron source with a spherical shell of "neutron-capturing stuff", you should get a fair chunk of them. Or convert whatever it is into isotopes.

 

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But I will capture them, lets say. How they will be released than, so they can be used in the chain reaction?

 

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If you capture a neutron, it's captured, and depending on what type of nuclide has captured it, it will stay captured.

Neutrons aren't like things you can store and forward so much, more dampen down or squelch.

 

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There is not fission with fast neutrons. Fast neutrons go through a nucleus too quickly to interact and be absorbed. No absorption: no unstable heavier nucleus and no resulting fission.

In a nuclear device, including power plants, the moderator, often heavy water, slows down the neutrons so they go slow enough to be in the nucleus for enough time to be absorbed. It is the half fast neutrons that are the active agents. The fast neutrons are ghosts that have little effect. The resulting heavier nucleus, if unstable, sooner or later fissions. The control rods are materials that absorb neutrons by forming heavier but relatively stable atoms. By absorbing neutrons and taking them off the playing field, fewer atoms absorb neutrons and become unstable.