Some applications that run Java do a better job than others of reporting out that they won't run with an un-secure version of Java. If I have a problem with a Java-based app, I immediately go to the java site to download and install the latest.
I remember for one practice we had to use an ancient version of Java for their hospital portal to work. Even though there were several reported security holes in that version. They stuck with it for years. It would absolutely not work with any version after that one.
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