The Gemara (Shabbat 33b) states:
מִשְׁפַּט רְשָׁעִים בְּגֵיהִנָּם שְׁנֵים עָשָׂר חֹדֶשׁ
the judgment of the wicked in Gehenna lasts for twelve months.
Is it only 12 months or longer and what happens to the wicked people after that time period?
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The Ramban in his sefer Sha'ar Ha'gemul writes here that those who are judged for punishment experience 12 months in Gehinnom in accordance with what they deserve. Following this, "נשמתן נשרפת והם נעשים אפר" - "Their souls are are burnt and made into ash".
The Ramban clarifies this to mean that their nature is altered, namely the soul is burnt and returned to ash, and then the רוח האלקים - the spirit of G-d takes it and scatters it under the feet of the righteous, which means that they are now in a state of neither suffering nor punishment.
So it would seem from the Ramban that their souls are elevated albeit not to a level of 'enjoyment', but rather to a stage devoid of any further suffering.
The wicked are punished by being denied the spiritual afterlife of olam haba. Some say they go to Gehennom (Gei Hinnom), a valley outside Jerusalem, and are punished there ('hell'), but this notion never received official sanction. It is also not eternal: “There will be no Gehennom in future times” (Talmud, Rosh Hashana 17a, Bava Metzia 58b, Nedarim 8b, Avodah Zara 3b).
The souls in Gehinnom are punished for up to 12 months, then continue on to Gan Eden (Eduyot 2:10). Those who remain wicked are annihilated (Rosh Hashanah 17a). The practice is to mourn for the deceased for only 11 months, so as not to imply that they needed the full 12 months.
The worst Jewish curse is "Yemach shemo vezichro" -- May his name and his memory be annihilated.