
zurückbleiben
to stay behind
To remain in a place while others leave.
Als alle Gäste gegangen waren, blieb er allein zurück, um aufzuräumen.
When all the guests had left, he stayed behind alone to clean up.
to stay behind / fall behind
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to stay behind
To remain in a place while others leave.
Als alle Gäste gegangen waren, blieb er allein zurück, um aufzuräumen.
When all the guests had left, he stayed behind alone to clean up.

to fall behind
To lag behind others in development, a competition, or performance.
Trotz Nachhilfe ist er in der Schule weit hinter seinen Mitschülern zurückgeblieben.
Despite tutoring, he has fallen far behind his classmates at school.

to remain
To be left over as a remainder.
Nach dem Brand ist vom Haus nur noch eine Ruine zurückgeblieben.
After the fire, only a ruin remained of the house.

please stand back
A formal announcement at train stations asking people to keep their distance from the platform edge.
Eine Durchsage ertönte: „An Gleis drei, bitte zurückbleiben!“
An announcement sounded: 'On platform three, please stand back!'
'Zurückbleiben' (to stay behind / fall behind) is a separable verb. The prefix 'zurück-' goes to the end in a main clause. In subordinate clauses and in the infinitive with 'zu,' the verb stays together.
Warum bleibst du immer zurück?
Why do you always fall behind?
The perfect tense of 'zurückbleiben' (to stay behind / fall behind) is always formed with the auxiliary verb 'sein' (to be), because it describes a change of place or state. So the correct form is 'ist zurückgeblieben' (has stayed behind / has fallen behind / has remained).
Nach dem Fest ist ein großes Chaos zurückgeblieben.
After the party, a huge mess remained.
In the figurative meaning 'to drop in performance,' 'zurückbleiben' (to fall behind) is often used with the preposition 'hinter' (behind) and the dative. You fall behind a person, a group, or an expectation.
Das Unternehmen ist technologisch hinter der Konkurrenz zurückgeblieben.
The company has fallen behind the competition technologically.
The command 'Bitte zurückbleiben!' (Please stand back!) in the imperative is a standard announcement at German train stations. It asks passengers to keep their distance from the platform edge when a train is arriving.
Am Bahnsteig ertönte die laute Durchsage: „Vorsicht am Gleis, bitte zurückbleiben!“
On the platform, the loud announcement sounded: 'Caution at the track, please stand back!'
to remain / to agree
Verbleiben formally indicates that someone continues to stay in a place. Zurückbleiben additionally emphasizes that others leave or do not come along. When this contrast is important, zurückbleiben is more suitable; without this focus, verbleiben can also be used in formal language.

Nach dem Ende der Sitzung blieb die Vorsitzende im Raum zurück, während die anderen gingen.
After the meeting ended, the chairwoman stayed behind in the room while the others left.
Nach dem Ende der Sitzung verblieb die Vorsitzende noch im Raum.
After the meeting ended, the chairwoman remained in the room.