Is there any version of (discrete) Morse Theory for subcomplexs?

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I am now working on the (discrete) Morse theory and its application about simplices and cell complexes. However, I cannot find any statement about the property on closed subcomplexes / submanifolds of the whole complexes or manifolds? It seems like there should be some relations since the subspace and its original spaces are closely connected and restricted. Can anyone provide any hints? Thanks!