Does liability decrease when company receives cash payment?

No, just because company receives cash does not mean that the liabilities will go down. Companies receive cash for merchandise sold, services rendered, money owed to the company from customers, investments, etc. These things will increase assets and either Revenue or Owners Equity (Stockholders equity) but they will not effect liabilities.

Liabilities generally refer to debts owed by the company, such as Accounts Payable, notes payable etc, which are decreased by the paying of cash, which in turn decreases Assets while decreasing Liabilities at the same time.

In some cases however, Liabilities can "increase" for a short period when a company receives cash. This happens when a company receives cash for a service or even merchandise that they have not supplied to the customer.

Example, say you are a watch manufacturer, you sale 2,000 watches to a customer but you won't actually ship the watches to the customer for say 30 days. That Unearned Revenue (cash) you receive is considered a liability until you actually fulfill your agreement with the customer. The reason for this is due to the fact that if anything happens and you can not fulfill the obligation, then you must repay the money to the customer, hence making it a short term liability. Once the obligation is fulfilled the money is recorded as Revenue and is no longer a liability to you.