In many cases it is where Thai women have married a farang (foreigner) and that relationship has long since ceased, but although permanently separated they are nonetheless still legally married. Perhaps her husband has long since returned to his native homeland, but they have never legally divorced, and haven’t heard from each other in years.
Firstly Australia does not currently recognise polygamous marriages. This is where there are two concurrent legal marriages. Therefore she would have to be legally divorced from her husband if you wanted to apply for a partner visa based on marriage.
She would also not be eligible to apply for an Australian prospective marriage visa (Australian fiancé visa) as one of the primary conditions of this visa is that it is a requirement that the applicant and sponsor have no impediment to marrying. Once a fiancé visa is granted, then the applicant has nine months from date of grant to travel to and remain in Australia. During this time both the applicant and sponsor must marry. After the marriage has taken place she would then apply for an onshore partner visa based on legal marriage.
The partner visa process is two stages. Firstly she would be granted temporary Australian permanent residency followed by permanent Australian residency if after two years the relationship was still continuing. However, given that she is still legally married, then this would be seen as an impediment and the fiancé visa would be refused from the outset.
If you were however able to prove that you are in a genuine and continuing de-facto relationship with your Thai girlfriend, then this itself would not be regarded as an impediment to lodging a partner visa based on de-facto relationship. However it is important to note that with any partner visa application it is essential that you can evidence that your relationship with your partner, whether legally married or de-facto is mutually exclusive, that is, it is a genuine and continuing relationship to the exclusion of all others.
This may prove to be very challenging and require the submission of substantial supporting documentation. The point is however that being in a legally recognised marriage with another person is not in itself an impediment to lodging a partner visa application based on de-facto relationship.