It's very commonplace for a corporation, when a sale is pending, to try to "freeze" hiring, until the new regime has taken over.
The idea is to keep the expense sheet as "constant" as possible throughout the transitional period. Suppose a sale takes a full year from start to finish, and within that year, your payroll expenses increase by 10 or 15%. The buyer would not be pleased, and could very well cut people once they're in control. It's better for both the buyer -- and the people who "could" be cut after the fact -- to institute a "freeze" until the sale is complete.
However, as many replies have stated, there are always exceptions. And in almost every case of a corporate-level sale, it's usually OK to replace people who leave, especially important positions. If a GM leaves, they'll replace the GM. If a key on-air talent leaves, they will be replaced too. But let's say you've got a station where only mornings and afternoons are live. It's doing pretty well and you've been thinking it's time to add a full-time live middayer. Not anymore!
Or let's say you have a sales "assistant" who leaves. They did basic crap like PowerPoint slides and other presentational materials... stuff the sales reps COULD do themselves, but it saves them a lot of time when someone else can do it for them. Well, those sales reps better get familiar with PowerPoint again real fast. Non-essential folks like this are among the types who may not be replaced during a hiring freeze. Same goes for the "remote gophers" who set up the cheesy tents, the Martis or Comrexes, prize wheels, banners, etc. If jocks can set up their own remotes in small markets, they can do it in big markets too... and there's another $20,000 salary restored to the bottom line.
To recap, if it's a job that could disappear without directly impacting the on-air image of the station, it will probably remain vacant during a hiring freeze. But obvious vacancies (like on-air talent) will usually be filled, especially if the station is doing well, and has a direct competitor in the same format. Same goes for major managerial positions which are essential to daily operations, like General Managers and the like.