The rounding should always follow the same rule. If the value ends in .01 or .02 then you round to .00. Doesn't matter if it's 10.01 rounding to 10.00 or 0.01 to 0.00.
The decision on what a company wants to do if an invoice total is $0.01 or $0.02 would be up to the company. The POS system should follow the rule and round to $0.00 if the method of payment is cash, but the company has the right to not give things away for free.
They can impose a minimum cash invoice amount of $0.05. But you would do this by requiring the customer to add more items to their purchase. You couldn't just round the invoice up to $0.05 and to charge them $0.05 for a $0.01 item
It would be similar to companies having a minimum purchase amount when paying by credit card. If their minimum amount is $10.00 and you want to buy something that's $5.00, you either pay cash or add something to your order. They don't just charge you $10.00 for your $5.00 item.
I think this would be a extreme edge case where you have an invoice with a total of $0.01 or $0.02, without any discounts, partial payments, etc.
If the customer's total was $10.01 and they paid with a $10.00 gift card, the final amount owing of $0.01 would round down to $0.00 and they wouldn't owe any more. If they had paid cash, the total would have rounded to $10.00 anyway.
Similarly, if the customer returned an item and bought a new item, or used coupons, and the total owing was $0.01 or $0.02, then you would round down to $0.00 and they wouldn't pay anything.
As BobbyScon said, you can implement some options to allow the company to decide how they want to handle this. You could have an option that doesn't allow a sale to be processed if the total amount is less than $0.03 and the sale doesn't include any discounts, returned items, coupons, etc. The option could be to completely block the sale, require a supervisor override, or just display a warning to the cashier.
Best bet is to talk to as many of your current or potential clients as you can to see how they would like this edge case handled. For many, it's probably a mute case since they wouldn't have items that have a unit price less than $0.03. Maybe a place like a hardware store that sells individual nuts, bolts, and washers.