Jaguar has withdrawn as the main sponsor of Coventry City's new stadium, which is due to be completed in August.
Coventry City FC are due to play at the stadium next season
The company said it has taken into account the "rapid deterioration" of its business situation.
In September, parent firm Ford announced that car production was to end at the city's Browns Lane factory.
The stadium will not now be known as the Jaguar Arena, but in a new deal the company is to sponsor the exhibition halls at the new site instead.
Coventry City Football Club are due to start playing at the stadium at the start of next season.
In a statement, Jaguar said it wanted to continue its commitment to the regeneration work which has been undertaken in the north of the city, where the arena is sited.
It says it also remains committed to broader, long-term support for the community, including links with the NSPCC, the Coventry Education Action Zone and the Coventry and Warwickshire Regeneration Forum.
Managing director of Jaguar Cars, Bibiana Boerio, said: "The Arena in Coventry is a significant development for the city and community and it is right that Jaguar be involved in some way."
Chief executive of Arena Coventry Ltd, Paul Fletcher, welcomed the continued involvement with Jaguar and said the stadium was still on course to open next summer.
He added: "We are confident that we will be in a position to announce a new naming rights partner in the not-too-distant future."
Under the plans to stop making XK and XJ Jaguars in Coventry, there will be 400 voluntary redundancies and 425 jobs will be moved to the Castle Bromwich factory in Birmingham.
Jaguar will also lose 750 mostly white-collar staff, as office work is merged with Land Rover.
The stadium project is a joint venture between the city council, the football club and other businesses.
As well as games, there will also be concerts, and dining and conference facilities at the venue.