Student Libby Squire was seen "crying and sobbing" in the street shortly before she disappeared, a murder trial has heard.
The 21-year-old went missing on 31 January 2019 after she was refused entry to a nightclub in Hull.
Sheffield Crown Court heard neighbours and passers-by had attempted to help Ms Squire on the evening of her disappearance
Pawel Relowicz, 26, denies rape and murder.
Prosecutors claim Mr Relowicz was "prowling the streets" of the city's student area in search of a target when he intercepted the "extremely vulnerable" Ms Squire.
He is accused of taking her to the secluded Oak Road Playing Fields and dumping her in the River Hull in the early hours of 1 February 2019.
Ms Squire's remains were recovered from the Humber Estuary seven weeks later.
Jurors heard from a series of witnesses who saw or spoke to Ms Squire after a taxi dropped her outside her shared house on Wellesley Avenue.
Passers-by Roland Jacobs and Alan Jones said they stopped when they saw her on the ground in the snow as they drove home from a darts match.
Passenger Mr Jacobs said Ms Squire had been "mumbling" and difficult to understand, and at one point had asked him "to come lay down with her".
When he refused her request for a hug, she began swearing at him and, after about 10 minutes, the men decided to "give up" attempts to help.
Student Jorge Thompson, who saw her exit the taxi, said Ms Squire "fell over face flat and was on the ground for 10 seconds".
"She was stumbling everywhere and struggling to walk," he said in a statement.
Ms Squire's neighbours, students Hannah Wright and Emma Halshaw, said they had invited her into their shared house when Ms Wright heard her "crying and sobbing" outside.
Another witness, Lorna Allen, described Ms Squire "lying on the floor and crying and screaming" near a bus stop shortly before midnight.
"She was slurring her words and talking to herself and she seemed very drunk," she said.
In her statement, Ms Allen said she had asked Ms Squire if she was all right but the student had "got up and staggered" away.
Extracts from her Ms Squire's medical records, detailing her history of mental health issues including depression, anxiety and self-harm, were read to the court.
Jurors heard she had researched methods for taking her own life, and had previously had suicidal thoughts which included "throwing herself in a river".
The trial continues.