It is possible as long as you have the global "Bulk Change" permission.
see: https://confluence.atlassian.com/display/JIRA/Managing+Global+Permissions
If you have that permission see https://confluence.atlassian.com/display/JIRA/Using+the+Issue+Navigator#UsingtheIssueNavigator-Workingwithissues
When performing bulk changes, the assignee is changed.. sometimes it seems to change based on the component lead. Is there a way to disable the assignee being changed?
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What kind of bulk change are you doing (edit, transition,move)?
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Move to another project? If yes, are all assignees of the current project also assignable user in the new project. Do you allow unassigned issues? If the last two answers are no, then you'll have your explanation.
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