The main issues are that (1) Oracle is a technology laggard in most of what it does, (2) its model is one of proprietary hardware/software in an increasingly open source and commodity world and (3) its core underpinnings are focused on relational database in an era when NoSQL and NewSQL is where the real innovation and growth is. As a result, many working for Oracle have a skillset mismatch with what the market is looking for.
It isn't that "Oracle" is on the resume that is the issue, but what that represents --- employees who are reasonably paid, but don't have the in-demand skills to justify that level of pay elsewhere. Other companies are growing and are hungry for good talent, but if one can't speak at some level of depth on technologies companies are using (e.g. NoSQL, Hadoop, nginx, Kafka, etc.) or the Cloud-based, distributed computing architectures or the hot trends (e.g. Machine Learning, IoT, etc.), landing a job outside of Oracle definitely will be difficult. It really comes down to making sure that one has marketplace value.
I found my way out of Oracle. During my own search, during my first couple of interviews I was hit hard by how the skills that were good enough within Oracle weren't anywhere close to what hiring companies wanted. As a result, I pulled back from interviewing and invested several months into learning -- taking online courses, reading case studies, looking at corporate engineering blogs, working through examples/tutorials/code samples, etc. -- in order to get into a more marketable position. It worked. I not only landed a job, but received a significant increase in compensation and benefits all within a culture that is radically better than Oracle's.
I know former Oracle colleagues who found their way out and their stories are all similar -- that they took charge of their own learning in order to avoid being trapped by how Oracle is increasingly becoming a legacy company. I now interview potential employees and, in general, I see that not having sufficient skills is a relatively common thing. For those coming from Oracle, I'd like to see them make it out, but the struggle in the interview is difficult to see. The on-premise, vertically scaling system/software that has been central to Oracle's efforts is so totally opposite from where the industry is moving that technical interviews often show a real lack of technical breadth and an inability to explain fundamental concepts or basic architecture. The culture is also damaging as the "tyranny of control" that flows from the top of Oracle erodes some of the key soft skills that are being evaluated in interviews. I believe that this, in part, is why some with long tenures at Oracle have resigned themselves to just try to hold onto what they have. If they can, then more power to them.
While it might be hard to land a job outside of Oracle, it isn't impossible. It does take some work and targeted effort to re-tool for the job one would like to land, but the payoff can be significant.