When do firms pursue the cost minimization objective instead of profit maximization? Are there any intuitive/practical examples/reasons? I understand that profit maximization implies cost minimization, that is, if a firm is maximizing profits, it will definitely minimize costs. 

However, under what conditions does cost minimization become an objective in itself?
Firms can be said to pursue cost minimization when they do not have control over demand of their product. In the short run, this implies also that unit prices are fixed. 

A standard example here is a Utility, say for electricity. Except in extreme situations of very high demand that reaches the network capacity, consumers consume electricity on demand for a given unit price or price schedule.  So "quantity produced" is not determined by the firm, and so the Cost-minimization problem is the most appropriate (minimize costs given output).