A welfare fraud investigator came to my home tonight. I wasn't there but he left his card. He showed his badge to my roommate and said he would be back. What is the process of an investigation? How long does it take? Could I be arrested by the police?
Possibly, yes, you could be arrested.
Be careful what you say to the investigator. They will use anything you say against you.
You would be wise to find an attorney that is familiar with these kinds of investigation to assist you, before you talk to anyone.
Be careful what you post on this or any other website. There is no confidentiality for postings here.
The only time you can be arrested is if there is a warrant for your arrest or "charges" have been brought against you. In that case, you would post bail and wait for further action. Remember that you have the right to remain silent and anything you say can and WILL BE held against you. Do not speak with anyone. Let them do their job. They are allowed to lie to you in order to get a confession.