We study how the effect of closed-string tachyon condensation can enter into the on-shell effective action of open-string tachyons, for bosonic case. We also consider open-string one-loop quantum corrections. We use the sigma-model approach with boundary terms, and we utilize some results of boundary string field theory (BSFT) to define the on-shell partition functions for open-strings. We regard D-instanton-like objects with appropriate weight as closed-string tachyon tadpoles, and we insert them into the worldsheet to analyze the effect of closed-string tachyons. The terms from such tadpoles diverge as well as those from one-loop quantum corrections, in general. However, it is already known that an appropriate choice of the weights cancels those divergences. We find this gives one of the natural choices of the weights of the closed-string tachyon tadpoles, which should be determined by some non-perturbative method rigorously.
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