As an employee of a start-up, what are the signs that we are about to be acquired?

Some signs include:

A sudden shift in priorities to things that make the numbers look good, especially the financial numbers. Suddenly efficiency, revenue and profit become the number one priority, while everything else gets neglected. They are trying to make the company more appealing for a buyout.
The owners or founders of the company suddenly take less interest in running the company and let their lieutenants run it for them. The owners may have better things to do, like negotiate the sale of the company.
People in suits show up, and tour the facility. They don’t appear to be sales people, since their demeanor is different and management usually doesn’t give sales people a tour. Sometimes management will even lie about who they are. (One company I was at claimed the visitors were people considering leasing a part of the building, but I recognized some of them from our competitor. They bought us out later.)
Management seems to participate in a lot of closed door meetings, much more than usual, and seems very secretive about it. They also seem to go on more trips than usual. They are most likely discussing the potential acquisition, and going to meetings off site.
You notice middle management start to be more conscious about their department’s performance, and start becoming more competitive with potential rivals. They know that if the acquisition occurs, there will probably be some reassignments and possibly layoffs. They are positioning themselves and their friends to survive the changes.

As you can see, most of the indicators are related to management suddenly behaving differently.

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