A put option gives the buyer the right but not the obligation to sell stock at some point in future (T).
A put option has the following payoff: max(K - F, 0)
F = Forward price; K = strike price
The forward price will (already) include the market's dividend expectation over the life of the contract.
All else equal, if the market suddenly revised its dividend expectations (e.g. because the company announced an unexpected upward revision in its dividend during the life of the contract) this would cause the price of the forward (F) to fall.
Why? Because the market would be expecting an even bigger drop to the stock price when the stock goes ex-dividend. As a result, the price of the put option would increase.
Finally, you asked: 'aren't we forgoing the dividends by holding the put option?'
Only stocks (and not options) accrue the actual dividend. The correct answer is that the dividend is embedded within the price of the put option. You could 'harvest it' by simiply purchasing the stock at the open on the ex-dividend date when the stock price would have dropped by the amount of the dividend. Have you made money? Probably not.
If you did make money you would have found yourself an arbritrage opportunity.
These ideas are fundamental in being able to master the option / derivative landscape.
I've intentionally tried to be succinct here. The ideas can take time to embed.
Happy to discuss.
Last edited: May 17, 2019