play possum

play possum (lie low to deceive sb; dissemble; feign ignorance (=pretend to be dead so that sb will not annoy or attack you)) — затихариться; залечь на дно
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From the habit of the common American marsupial (properly 'opossum') of lying as if dead when under threat.

сf.:
[keep a low profile]
[lay low for a while]
[залечь на дно]