= Solution
Assume independent individuals and <independent censoring>: conditional on any modelled covariates, the censoring mechanism gives no additional information about the latent event time and has no parameter shared with its <survival distribution>. An observed event at $x_i$ contributes the <probability density function> $f(x_i)$. A <right-censored> observation contributes the <survivor function> $F(x_i)$, since it establishes only $T_i>x_i$.
More formally, let $C_i$ be an independent censoring time with density $c_i$ and <survivor function> $G_i$. The observed pair $X_i=\min(T_i,C_i)$, $v_i=\mathbf1_{\{T_i\leq C_i\}}$ has a parameter-dependent factor $f(x_i)G_i(x_i)$ if $v_i=1$ and $F(x_i)c_i(x_i)$ if $v_i=0$. The factors involving only the censoring distribution can be omitted from the event-time <likelihood>. Thus
$$
L=\prod_{i=1}^n f(x_i)^{v_i}F(x_i)^{1-v_i},
\qquad
\boxed{\ell=\sum_{i=1}^n\{v_i\log f(x_i)+(1-v_i)\log F(x_i)\}.}
$$
Using $f=hF$ also gives the useful <survival likelihood> form
$$
\ell=\sum_i\{v_i\log h(x_i)-H(x_i)\}.
$$
Every individual therefore contributes survival exposure, whether or not an event is observed. These formulas do not justify ignoring <informative censoring>; that situation requires a model for the observation mechanism as well.
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