I'm not sure if this is a misunderstanding or just a matter of scientific terminology, but the "star cycle" is not something you can "drastically change".
The life cycle of a star (as we currently understand it) is a fairly predictable set of stages of evolution from the formation of a star from a cloud of gas, along the main sequence (the stable stage out own star is currently in) and then to "death" of the star as it's internal fuel runs out, and material can be released back to the interstellar medium.
For more details see the Wikipedia page, this video from NASA, or this very simplified diagram from the BBC.
But to answer the underlying question, stars at different stages of their life cycle can definitely affect other stars, planetary systems, or interstellar matter that is nearby in many ways. Here are a few examples:
- When young stars are born they may be quite close together and their mutual gravitational forces will disrupt circumstellar disks (where planets form), which may inhibit the formation of planets, but the specifics of this are debated in the scientific community.(see this paper)
- At the end of their life cycle, more massive stars may explode in a supernova, which releases lots of energy and throws matter out. This can change the structure of clouds of gas and can compress it, possibly triggering new stars to form in the more dense material. This is also a topic of current study so the exact details and mechanisms are not very well understood, but the theory is logical and observations have been found that seem to confirm this.(see this paper)
- A white dwarf star and a red giant star in a binary system can have transfer of mass from the red giant to the white dwarf. A white dwarf has a maximum stable mass (Chandrasekhar limit) so when the mass exceeds this, the white dwarf will go supernova - this is , as you stated, a drastic change in one star due to interaction with another star.
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