How can you that to start a debate. Obviously, and logically, if the person is under-employed then his/her problem is not if/when/how to buy Bitcoin, but where and how to find his/her next job. Plus such a person would develop mental insanity with Bitcoin's volatility if all of his/her rent and shopping money is held Bitcoin. That person will be forced to sell.
By under-employment I mean people whose salary is just enough for their basic needs and little savings but not enough to afford privileges like vacation, luxuries, even buying a house as they can only rent. Such people spend as much as 80% of their income on food, rent, school fees of children and normal healthcare but not serious surgeries. People at that stage easily resort to borrowing when they have serious emergencies which do not come always though. Unfortunately, majority of workers in my country fall into this category. Minimum wage in my country is about $30 with inflation at 29%, a country of 200 million people that have over 83 million people living below $2.5 per day. So my use of that word is a reflection of the realities on ground here.
Under this circumstances, the best an individual can do is inject max 10% of their income to Bitcoin while setting up emergency fund with the remaining 10% since 80% is already expected to be used for basic needs. These are just my estimations, there could be variations.
Well I don't see any reason why someone who has no money to spare should think of investing, shouldn't he get an extra job or something, I get things are though but some though and unprepared decisions would put you in even thougher situations. Anyone can invest as long as they have good cashflow management and a source of income, but in this case where the income is really small, I think its better he start by building up funds by savings, maybe 3 months to six months of emergency funds before he thinks of allocating any amount to DCA, and if he really want to build a substantial amount of BTC holdings then he must increase his income, cause that income can only carry him that far.
Under-employed can still do $10 per week and still be fine with his needs. That one is under-employed does not mean he has no way of saving a little, just that such a person cannot do certain things that money can do because of financial limitations but nothing beats humble beginning. As a matter of fact, they even need the investment more if they have to remedy their situation.
Allocating 10$ isn't bad, but from your previous figure I think 10% of that should be 3$ and thus would be really small of he plans on building his emergency funds too. Not all humble beginnings are really wise, I don't think investing is the best advice for low earners, especially when they don't have any back up funds.