The number of unfinished stories (preferably zero) seems to be used as a major indicator for a good running agile team. It is regarded important enough to put incentives on it (I’ll bring beer/a cake if you guys succeed) or to start making pressure like: “We didn’t finish 5 stories in the last sprint. We have to get better. Don’t let that happen again in the next sprint!”
Unfinished stories certainly show that something is not working as the SCRUM doctrine mandates. But ask if it is an indication of obstacles. Ask if the team perceives it as a problem. After all most teams live in a real world where things are not perfect. Unfinished stories might not be an issue at all for the version of agile a particular team lives.
Pressure towards “no unfinished stories” will likely cause the team to find ways to report finished stories. The story scope can be changed during the sprint. Not quite finished stories might simply be marked as done. As long as mere book keeping tricks are used the harm of such pressure is limited, although some effort is wasted. However the effects go further. If a good idea arises during the sprint it might get suppressed. Reviews might get relaxed in order to not push a story over to the next sprint. Anything that causes unforeseen but justified additional work will be seen with reluctance.
This behavior might reduce the number of unfinished stories but it weakens the team and is counter productive in the end. In addition the “unfinished stories” - indicator becomes useless. I’d go as far as to say that if a team consistently has no unfinished stories it is either exceptional (and you should feel the vibes anywhere near them) or, more likely, something is going wrong.
So please embrace unfinished stories as an indication of possible problems. Try to fix the underlying cause and watch the unfinished stories disappear. But it might turn out that there are valid reasons for that particular setup to result in unfinished stories. In that case relax and and let the team focus on it’s work.