I thought I should post this to warm people to be careful what they say at immigration.
A buddy of mine on the standard humanities/int'l services work visa who got laid off was collecting unemployment insurance payments from Hello Work and has since been working part time while searching for a job. He went to the immigration info desk to ask some questions about renewing his visa and mentioned his part-time work to the lady there and he said she went ape-shit and was almost yelling at him that he can't do that on his visa he needed to go directly upstairs and report this to immigration officials and apply for a change in status. Not wanting to get in trouble he said OK but just left instead and luckily she didn't blow a whistle and have security tackle him or anything like that.
I'm on the same kind of visa and was also collecting unemployment last year while working part time. I had to report this to Hello Work because your unemployment is adjusted based on how many hours you work. Plus I was being taxed on it and even filed a tax return this year. Of course, no one's knocking at my door looking to deport me and I'm sure I'll have no trouble renewing my visa in a couple of months now that I'm working fulltime again, so it seems like none of the government agencies are communicating with each other and no one outside of immigration cares about immigration law.