Hi inlaw,
if you are still working in the same location,doing the same job,under the same conditions prior to the change of ownership then you are totally fine and you should continue working there,the new owner does not need to get an LMO because this is only a change of ownership and not employer.
so as you stated you are still working for subway meaning the operation name is the same the only thing that has changed so far is the corporate name.
CIC allow foreign workers to continue their jobs in the cases of (acquisition,merger,consolidation) as this happen often and it should has no impact on foreign workers in canada under LMO or intra-company transfer as long as the new owner is seen as a succesor of interest to the previous one( meaning the new ownership succed to the interest of the previous ownership).
what you need to do now is send an application to reflect the name of the employer on your work permit,for this you need to pay the work permit fees and attach a statutory declaration from your employer attesting to the nature of the change and explain the succesor of interest after the takeover of the business by the new owner along with a press release if there is any(this is not must but its to the best of your interest to keep cic informed about the new changes that took place so it will be updated in their database and prevent any delay in the future if you apply for pr).
once again no LMO is needed and you don't need to stop your job as you are not doing anything illegal.
if you want more info about this visit the temporary foreign workers operational manual and you will find details under the mergers,acquisitions and consolidations chapter.
good luck.
