A Rabbinical question (She-elah) was asked concerning those who light the Shabbath candles using oil instead of candles. Some people would put in a lot of oil, so that they would burn throughout the day of Shabbath into the following evening. Is there a basis for this custom?
It says in a responsum in Torah Lishmah that there does not appear to be any source for this custom. The reason a light is kept burning throughout the day in a Synagogue is for the honor of the Synagogue. A memorial (Yahrzeit) candle remains burning throughout the day for the soul of the one who passed away. However, keeping a light burning throughout the day on Shabbath in a person's home, serves no purpose.
On the contrary, it comes under the prohibition of Bal Tash-hith (wasting), and should be stopped.
(See Torah Lishmah, Orah Hayyim, She-elah 'Ahn Waw)