Hmm, how do commies propose to remove people's individual property rights without their consent, and how will compliance be forced?
I'm not a communist, I'm an anarchist, but I'll answer your question all the same. When you talk about individual property rights you are talking about the rights of some individuals at the expense of others. The French anarchist Pierre Joseph Proudhon said, in 1840, "Property is theft!" and what he meant by that was if, for example, I need a place to live and have little money, I will have to rent a house- and this means that someone is exploiting my basic need, shelter, by forcing me to pay him for it. That's downright
authoritarian.
If I work for someone I will have to submit to their commands because they "own" the business. I will have to accept the wages thye give me even though
wages do not represent how much work you do- they represent how much money the employer has to pay you in order for you to keep working there. If they could they would pay you nothing. It's a one-sided, parasitic relationship.
But because one of my most basic human needs, the ability to feed and clothe myself, is only attainable through working for someone else under capitalism, I have no choice. That sounds pretty dictatorial as well.
Under capitalism, if I do not own anything I can sell I will have to sell myself, my body, to someone who does own property. It is another form of slavery, and actually a more efficient form for the bosses because they no longer have to cook for you, clothe you, or house you.
I think you believe in liberty- that's good, so do I. If you do believe in liberty why do you support this new form of slavery where some people must work for others?
As far as your original question- if by individual property rights you mean a family with a farm, a craftsman working out of his own house, a self-employed computer programmer doing his thing- that's fine. We would let them be and even help them if they needed it. The anarcho-syndicalists of Catalonia respected the right of individual farmers to be left alone.
All anarchist communes and cooperatives would be voluntary efforts that would encourage by example- these cooperatives would have no bosses and would decide what to do on a democratic and participatory basis- we would hope that people would like the idea and try it themselves.
However, if you talk of a larger business enterprise where people worked not for themselves but for other people, the tyrannical slavery I talked of earlier, we would assume that no worker, given the choice between working for a boss and being hungry all the time
or working without a boss with others on an equal footing (or alone) would choose the boss. People would simply refuse to work for the capitalists. We wouldn't need to opress them or anything, just refuse to be their slaves.