There is no actual partial share, but from a probability standpoint, there is the same effect. If it takes you 30 seconds on average to find a share, and I give you a 30 second time limit to find one, 50% of the time you will, 50% of the time you wont. If i give you 50 seconds to find one, more often than not you will, but there will still be plenty of occasions where it will take longer than 50 seconds and you wont make it.
Its probability. Probability isn't very useful with a sample size of ONE, which is what you keep trying to use as an example. The useful ness of probability becomes greater the greater the sample you use it on.
If the average time to find a share was significantly longer than the block time OF COURSE you would get nearly 0 of your hash rate. Think about that. If it takes you one minute to find a share on average and the block changes every 10 seconds, you have a race condition you are only going to win about 1/12* times.
I think you either don't quite understand probabilities or how pools work. Looking for shares is completely independent of the past. Your chance to find a share in that time may be relatively low, but since the difficulty is so large, your reward is proportionally higher.
The probability of a certain number of independent events in a certain time is given by the
Poisson distribution. Let's assume you submit on average 1 share per new block. Then
here are the probability for actually finding X shares in that time. Now, assuming we now switch to 10x the previous diff. Of course, it will be unlikely that you submit a share in that time, but it is in no way impossible.
Here is the distribution of shares found for that case. So you have about a 10% chance of finding a share (slightly less, because you also have a tiny chance of finding more than one share). However, that share is worth 10x as much so it evens out.