How Jira status will get change(based on build status) after build is triggered in jenkins from Jira ? If build is failed then Jira status should automatically change to failed state and vise versa.
I believe that you can do it from Jenkins side.
Create a script which runs after the build in Jenkins; which gets the build result and change status of the issue in Jira through Jira REST API.
You can find the REST API method for status change ("transition an issue") from this link.