= Solution
Under <independent censoring> conditional on the modelled <covariates>, an observed event contributes $f_i(x_i)=h_i(x_i)e^{-H_i(x_i)}$, and a right-censored observation contributes $S_i(x_i)=e^{-H_i(x_i)}$. Factors from the censoring distribution may be omitted when they contain no survival-model parameters. The <survival likelihood> and <log-likelihood> are therefore
$$
\boxed{L=\prod_i h_i(x_i)^{v_i}e^{-H_i(x_i)},\qquad
\ell=\sum_i v_i\log h_i(x_i)-\sum_iH_i(x_i).}
$$
Censored individuals still contribute their observed exposure through $H_i(x_i)$; they are not deleted from the analysis.
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