Switching field after a PhD in math
I don't have any statistics about how common it is, but that shouldn't really concern you. The more important question is whether it is possible. 

I assume, without statistics, that in a competitive job market that many people must, in fact, change their direction. If there are too few jobs then people must look elsewhere or find a way to be more competitive themselves. 

The issue you face is really only finding a job. To do that you have to be attractive to the ones offering the job. Math is a great background on which to build as it gives you analytic and deductive skills that can be brought to bear on many problems. But you can also appear over-qualified for some positions. 

But if you want to work in specific fields, you probably need to get some qualification in those fields, even if it is pretty informal. Employers probably don't want to support you while you learn if it takes too long and there are other, better qualified, candidates. 

Some applied math or statistics might put you in a better position. 

But you need to search out jobs, selecting those that best fit your skills, but also finding a way to promote your skills as appropriate. 

You might, in fact, look for a "bridge" position, say as a postdoc, that gives you time and an opportunity to get some qualifications in an applied field that appeals to you.