The most obvious method of avoidance is to purchase many small items from different vendors. If you can get enough credit to buy something of value, while remaining below the threshold at which people will sue you, you can never be forced into paying a bill. The problem is figuring out what level this is. Very few people will sue you for under $100, because the suit fees exceed the maximum you can gain in the process. From $100 to $500, creditors vary. Above $500, most creditors will sue you. In other words, you have to take enough to make it worth taking, while not taking so much that it's worth chasing you.
From a collections standpoint, it is to your advantage to have a credit agreement that awards reasonable legal fees, costs, interest, and penalties in the case of a failure to pay. This makes it far more cost effective to pursue a case through the legal process, and punishes the debtor for not paying. If you come across a debtor that does this regularly, you may also be able to get the police to arrest them for fraud. If your credit request papers are properly designed, there may be laws against making false representations on these statements as well, depending on the nature of the statements and how they are used. You might make it a policy to only allow credit for amounts above some threshold (perhaps $100) to make it worthwhile to pursue debtors. At $500, it is almost always worth pursuing debtors, but for many businesses, this is far more than the normal purchase price, and their customers stay with them because of their credit policies.
One very strong counter to the debtor who takes a little from a lot of people is the use of credit bureaus and consolidation of debts from many creditors. This is usually beyond the scope of a small business, and is far better done by a lawyer who specializes in collections.