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Standard extractive systems suffer from the lack of gold training signals since existing corpora solely provide document and human-written summary pairs while disregarding extractive labels. As a result, existing methods resort to imperfect pseudo-labels that are both biased and error-prone, thereby hindering the learning process of extractive models. In contrast, text generators which are commonly employed in abstractive summarization can effortlessly overcome this predicament on account of flexible sequence-to-sequence architectures. Motivated to bypass this inherent limitation, we investigate the possibility of conducting extractive summarization with text generators. Through extensive experiments covering six summarization benchmarks, we show that high-quality extractive summaries can be assembled via approximating the outputs (abstractive summaries) of these generators. Moreover, we find that the approximate summaries correlate positively with the auxiliary summaries (i.e. a better generator enables the production of better extractive summaries). Our results signify a new paradigm for training extractive summarizers i.e. learning with generation (abstractive) objectives rather than extractive schemes.