I'm not sure what you are asking here. The first 3 months of any new nursing position is generally a trial period, called the probationary period in my parts. The facility may decide to terminate at any point they don't feel the nurse is a good fit for the position. But Texas is an employment at will state...here we can be terminated for just about any reason as long as its not blatantly violating federal law.
Check your own state employment laws regarding termination practices...if it is not an employment at will state, it may be harder to fire someone.
Are you concerned you will start orienting somewhere and they will let you go? Most facilities don't waste their time training someone if they don't intend to try to keep them. But there are exceptions: the nurse who is too slow, doesn't catch on, isn't motivated, poor people skills, etc. I've seen this happen occasionally...but if one is actively working and succeeding in meeting goals and getting constructive feedback in orientation it is unlikely.
Sometimes the employee or the employer will decide the job is not a 'good fit' for whatever reason, and it doesn't work out.
Hope this helps but not sure if I'm answering your question.