When a company buys out another company, they are not buying the employees. They are buying the business. You and all the other employees will be officially terminated from XYZ company. You, after your last day of employment file for unemployment benefits. Whether or not you have been offered a job by the other company is not the decider on whether you qualify. You must qualify monetarily, which means you have made enough wages in the quarters they are looking at right at the time you file. This is individual for each person who files.
If you meet the monetary criteria, you must also be out of work through no fault of your own. Your company has closed, so you are out of work through no fault of your own. That a new company, ABC has allowed the old employees of XYZ to fill out applications (if they want to) at their company is not relevant.
In order to be eligible for unemployment benefits, you must be able and available for equivalent work. If ABC actually calls you up and offers you a job with the new company, then at that point, you will decide if you wish to accept it.
Since unemployment benefits do not last very long, regardless of your situation, and because they do not provide as much money as working would provide you, it is strongly suggested that you are in a search for an acceptable replacement job. If the job you have been OFFERED at the new business place of the ABC company is not equivalent, (and to know this, you must know the specifics, what salary, duties, etc. it would involve, and you must have been actually offered [U]the job[/U], not just a chance to fill out an application) at that point you would decide whether or not you wanted to accept.
And if you decided you didn't want the job, that it was too far from your home to accept, you think you will be able to find a job closer to home that will be better for you, you would report this job refusal to the unemployment system and they would make a decision about whether or not it would be considered an acceptable equivalent job. If it was, and you'd turned it down, that might stop your receiving any further unemployment benefits.
But in the scenario you have described, you just go on and file for benefits and wait to see what happens. There's no "Yes, you will" or "No, you won't" qualify for unemployment under any circumstances. It costs nothing and there's no downside to applying for benefits.