For American options assuming that the underlying is trading and reasonably liquid, no. That won't happen. Otherwise one would buy a put, buy shares, and immediately exercise the put... Or hold both and see if the share price goes above the put strike by expiration...sell both of it does.
Theoretically it may happen. The option price considers the FORWARD price and not the SPOT price (1.15 in your case), though most of the time they are almost equal. Say by some reason, the market is 100% sure that future price will be 2x the current spot price at expiry, so FORWARD = 2.3, then the put at 1.5 would be priced at zero (maybe have a 0.01 ASK on it but no bid). Now why the heck forward would go up unless there's a 2x split going on, and in that case, the strike of 1.5 would be actually 3? No idea, it's common occurence for forward to be less than spot when a dividend payment is due. The reverse, FWD > SPOT ... anyone has a legitimate reason for it? Actually thought about it a little and answered it myself. It's the contango case and it happens for assets that are more pricey to hold as stock than futures. Think perishable commodities like soybeans. In this case you may buy them SPOT now for say $1.15 a ton, minimum 100 tons. But what the heck do you do with them until the put contract expires, where do you keep them? Someone holds these soybeans in a warehouse and they sell the future on them for 2x the spot price. Want those soybeans in a year from now? Pay $2.3 on a futures contract! Else you are free to hold them yourself for a year and then deliver them if you can. So in this case FORWARD > SPOT and put price at strike 1.5 with maturity in a year will be LESS than STRIKE - SPOT.