Hi and welcome to JustAnswer,Thank you for the question and your patience. Should you still need assistance for information purposes only...Initially, bear with us; re-confirm and post back with the complete model number of the "...Insignia wireless headphones..."
Additionally, please post back with clear closeup pictures of the left earmuff and the base where it was detached from. Click HERE.
Still, in some instances and depending on the failure point, it may be possible to rig a workaround fix which may require the use of super adhesives.
Alternatively and should you be uncomfortable with a DIY (do-it-yourself) repair approach, perhaps your best bet would then be to consult with and/or seek the services of an authorized Service Center (specially if still under some form of extended warranty). Call 1-***-***-****.
Please post back how you would want to approach this and/or should additional information be needed.