The thing becomes the subject
With the se de involuntariedad (accidental se), the subject is not the person but the thing something happens to. The person appears as an indirect object: it happened to them. That is why the verb agrees with the thing, not with the person.
The pattern
Se me cayó el vaso.
I dropped the glass.
Se me cayeron las llaves.
I dropped my keys.
plural, because there are several keys
A Juan se le olvidó la cartera en el taxi.
Juan left his wallet in the taxi.
Se nos ha hecho tarde.
It's got late on us.
fixed phrase with no thing as subject
Typical verbs
Whose fault is it? Choosing the form
Both forms are correct. With the person as subject you own the action, and it may even sound deliberate. With se + pronoun you present it as an accident. English mostly keeps the person as subject (I dropped it, I forgot) and adds accidentally when it matters. Spanish builds the accident into the grammar.
Same shards, different message
Person as subject
He roto tu jarrón.
I've broken your vase.
I own up to it.
Olvidé la cita con el dentista.
I forgot the dentist appointment.
se + pronoun
Se me ha roto tu jarrón.
Your vase got broken.
It just happened.
Se me olvidó la cita con el dentista.
The dentist appointment slipped my mind.
The same pattern works for thoughts: Se me ocurre una idea means "An idea occurs to me". The idea is the subject; you are just where it turns up.
Another se: all of it
With verbs like comer, beber, leer, saber or ver, a se (or me, te …) can stress that the action was carried out completely, often with a hint of enjoyment or excess, much like English up or through in eat up, read through. The object is then bounded: a specific thing or an exact amount. With unspecified amounts (Comí pizza) there is usually no se.
Neutral or complete
Without se
Comió tarta en la fiesta.
He had some cake at the party.
Leí la novela en vacaciones.
I read the novel on holiday.
With se
Se comió toda la tarta.
He ate up the whole cake.
Me leí la novela en dos días.
I got through the novel in two days.
Se sabe el discurso de memoria.
She knows the speech by heart.
Anoche nos vimos tres capítulos seguidos.
Last night we binged three episodes in a row.
colloquial