Is there any case in which Liability increases and decreases as well?

In one single transaction there are absolutely NO chances that liability increases and also decreases at the same time. And even for the sake of argument we consider that yes it will increase and decrease then the increase and decrease will be equal thus making no difference at all.

However, if the question was asked about two different liability accounts, then yes it is absolutely possible. There are number of examples in which one liability account increases and other decreases.
For example:

• a creditor to whom we owed some money, we issued a promissory note to him, thus creditor’s account will decrease and accounts payable account will increase.
• Similarly, if one promissory note expires or if old promissory note is renewed then the same will happen.
• Also, if one creditor is paid through credit card, then liability towards creditor will reduce and towards bank will raise with equal amount (ignoring the effect of interest, if any).

But again, liability account and liability itself are two different things. Liability itself refers to total liability according to accounting equation and liability accounts are different recording points under liability. So, one account can increase and one can increase but the total liability will remain unaffected.

Example:

At the period end company owed 15,000 to certain creditors. Its financial position is as follows:

Company decided to pay one of its creditors through by taking loan from the bank. Company took 10,000 loan from bank and paid the creditor. Due to this transaction liability towards creditor was eliminated but liability towards bank increased.

After this transaction the financial position can be stated as follows:

As you can see the total liability amount is still 15,000 but in one transaction two liability accounts are affected in equal and opposite manner i.e. creditors account decreased and loan account increased by 10,000.