Is there a verb for remaining silent?
Dutch has the verb zwijgen, which means remaining silent. Ik zwijg means I remain silent or I say nothing. It is also often used as an imperative, similar to shut up.
I have been discussing this with some native English speakers who have sound understanding of Dutch, and we couldn't come up with a verb in English.
Does it exist?
There is no single word to capture exactly what you're looking for.
First, the difficulties with some suggestions. You're looking for a single word for 'to remain silent'. Forcing in to a single word, the semantic nearby shorter terms don't really capture this well.
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'To silence' is a transitive verb — someone is making someone else be quiet. You can say 'to silence oneself' but that has a special ring to it, a very active restraint, too forceful.
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'Hush' is a command — it is rare in the non-imperative and then it is a transitive like 'to silence'.
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'Shut up' is very much a command like 'hush' and is a bit forceful and rude.
Now for the closest 'way' to say it. The translation of German 'schweigen'/Dutch 'zwijgen'/French 'se taire' is matched best by
'to keep quiet' or 'to remain quiet'.
which is an intransitive statement of state. For example:
"I was told it was a secret so I kept quiet"
"If my boss brings up the incident I'll remain quiet"
Other more colloquial phrasings are 'to keep ones mouth shut' or 'to keep mum'. All these can be used in an imperative manner but don't have to be.
hush (hʌʃ)
interj., v. hushed, hush•ing,
n. interj.
- (used as a command to be silent or quiet.) v.i.
- to become or be silent or quiet. v.t.
- to make silent; silence.
- to suppress mention of; keep concealed (often fol. by up): to hush up a scandal.
- to calm, quiet, or allay: to hush someone's fears. n.
- silence or quiet, esp. after noise; stillness.
[1350–1400; appar. back formation from husht whist2 (Middle English huissht), the -t being taken for past participle suffix]
Random House Kernerman Webster's College Dictionary, © 2010 K Dictionaries Ltd. Copyright 2005, 1997, 1991 by Random House, Inc. All rights reserved.
In British English, schtum is an informal adjective used to mean remaining silent, e.g.:
It's for the best if nobody hears about any of this business, so if you're asked, make sure to keep schtum.
Although I've personally never heard it used as such, according to Oxford Dictionaries.com schtum can also be used as a verb:
Be or become quiet and non-communicative
The definition page provides a few examples, but I think the following is the most apt to the case provided in the question:
The possible risk being that she schtums and won't tell me the truth or just laughs in my face when I bring it up because it's apparently trivial.
This usage in the active voice sounds pretty jarring to my ear, though. Although I'd probably still think it an unusual word-choice, another example taken from Oxford Dictionaries.com utilising the passive voice sounds far more idiomatic:
This source was schtummed when Julia posted a scathing rebuke on the thread, really very angry.
The word schtum on its own can also be used in the imperative/as an interjection:
Schtum!
Used as an imperative, schtum is not directly equivalent to the example of shut-up given in the question (in the sense of an interjectory command for "Silence!"). Its meaning is more akin to "keeping quiet" about something in the sense of not releasing information.