Your case in NLRC will prosper even if you don't have any supported documents of your appointment for as long you can present substantial proof that there exist an employer-employee relationship between you and the employer. In the absence of any contract, for as long the company has selected you to work for them, they are the ones paying your salary, they have the power to dismiss you anytime and they have the power of control over you in the manner of what and how you work, then the court will always regard you as their employee and you can only be dismissed if the company has complied with the twin-notice rule requirement.
The twin notice requirement is explained in the case of Nitto Enterprises vs NLRC [G.R. No. L-114337. September 29, 1995.], to wit:
“There is an abundance of cases wherein the Court ruled that the twin requirements of due process, substantive and procedural, must be complied with, before valid dismissal exists. Without which, the dismissal becomes void.The twin requirements of notice and hearing constitute the essential elements of due process. This simply means that the employer shall afford the worker ample opportunity to be heard and to defend himself with the assistance of his representative, if he so desires. Ample opportunity connotes every kind of assistance that management must accord the employee to enable him to prepare adequately for his defense including legal representation.
Also in the case of Pepsi-Cola Bottling Co., Inc. v. NLRC:
“The law requires that the employer must furnish the worker sought to be dismissed with two (2) written notices before termination of employee can be legally effected: (1) notice which apprises the employee of the particular acts or omissions for which his dismissal is sought, and (2) the subsequent notice which informs the employee of the employer’s decision to dismiss him (Sec. 13, BP130, Sec. 2-6 Rule XIV, Book V, Rules and Regulations Implementing the Labor Code as amended). Failure to comply with the requirements taints the dismissal with illegality. This procedure is mandatory; in the absence of which, any judgment reached by management is void and inexistent (Tingson, Jr. vs. NLRC, 185 SCRA 498 ; National Service Corp. vs. NLRC, 168 SCRA 122, Ruffy vs. NLRC. 182 SCRA 365 L ).”
With regard to the lost items, you cannot be held liable to pay for that for as long as there is no negligence or fault on your part as a custodian. Since the company's stand is to make you liable for the lost items, most probably they will file a civil case to recover damages from you. Remember you are not the owner of that lost items but the company is. You just have to present proof that you have performed your duties and responsibilities as a custodian and you were not negligent and no fault can be attributed to you.
Note: This is just from a mere point of view of mine being a law student since I just finished taking up Labor laws subject. Much better to consult a lawyer for his legal opinions for this matter.