Can the history be a subject to General Grounds for Refusal?

Guys
I have a question:
Situation:
Someone lived in the UK on asylum status more than 15 years ago. During that time she was supported from the public funds (Social Security), and she never broke the UK law. Her asylum application was not successful, and she left the UK after receiving a relevant request from the Home Office. This was not a deportation order.
Now she scores enough points to be qualified as the Skilled Immigrant (Tier 1), but heard that even so, her application can be refused based on her past.
Question:
Will her UK's asylum past prevent the Tier 1 application from to be successful? In other words: can it be a subject to General Grounds for Refusal (such as: "she will use the public funds again", or "she will not leave after her working visa is expired")?
Has a someone from the this forum came across with such situation?
Thanks to all who replies.

It wont affect her application. All she needs to do is to declare all this in the relevant section of the application form.